113

Energy13

Many13Slides13Are 13From13Prof13Tom13Murphy13(with13Permission)13Thank13You13Prof13Murphy13

Course Preview the Big Picture13

bull  We use a heck of a lot of energy13ndash  primitive society uses lt 100 W of power per person13ndash  our modern society burns 10000 W per person13ndash  surely not in our homes Where is this going on13

bull  Energy availability has enabled us to focus on higher-level issues as a society13ndash  art13ndash  science13ndash  home shopping network13

213

bull  Long ago almost all of our energy came from food (delivering muscle power) and almost all our energy went into securing food for ourselves13

bull  Enter the work animal supplementing our muscle power and enabling larger-scale agriculture13

bull  Next burn wood to run boilers trains13bull  150 years ago muscular effort and firewood

provided most of our energymdashand today this is less than 1 of the story13

bull  Today much more energy goes into growingharvesting food than comes out of food13

bull  Today in US 86 of our energy comes from fossil fuels (oilnatural gas coal)13

Fuzzy on the concept of energy13

bull  Donrsquot worrymdashwersquoll cover that13

313

A note on graphs log vs linear13bull  Many graphs are on logarithmic scales watch for this13bull  This condenses wide-ranging information into a compact

area13bull  Pay attention because you could warp your intuition if you

donrsquot appreciate the scale13bull  Log scales work in factors of ten13bull  A given vertical span represents a constant ratio (eg

factor of ten factor of two etc)13bull  An exponential increase looks like a straight line on a

logarithmic scale13

413

Example Plots13

Exponential plot is curved on linear scale and straight on a logarithmic scale

513

A brief history of fossil fuels13

bull  Here today gone tomorrow13bull  What will our future hold13

ndash  Will it be back to a simple life13ndash  Or will we find new ways to produce all the energy we want13ndash  Or will it be somewhere in the middle13

Global Energy Where Does it Come From13

Source131018 Joulesyr13

(~QBtuyr)13Percent of

Total13Petroleum13 15813 40013Coal13 9213 23213Natural Gas13 8913 22513Hydroelectric13 28713 7213Nuclear Energy13 2613 6613Biomass (burning)13 1613 0413Geothermal13 0513 01313Wind13 01313 00313Solar Direct13 00313 000813Sun Abs by Earth13 200000013

then radiated away13

Ultimately derived from our sun

Courtesy David Bodansky (UW)

613

713

Why do we use so much energy13

813

913

We live in a special time and placehellip13bull  We use almost 100 times the amount used by the rest of the

world (by population)13bull  This phase has only lasted for the last century or so13bull  Most of our resources come from fossil fuels presently and

this has a short finite lifetime13bull  Fossil fuels formed from solar energy over 300 million

years will be used up in a few centuries13

2000 2500 3000 3500 4000 1500 1000 500 0

year

ener

gy u

sage

1013

Energy the capacity to do work13

bull  This notion makes sense even in a colloquial context13ndash  hard to get work done when yoursquore wiped out

(low on energy)13ndash work makes you tired yoursquove used up energy13

bull  But we can make this definition of energy much more precise by specifying exactly what we mean by work13

Work =Energy more than just unpleasant tasks13

bull  In physics the definition of work is the application of a force through a distance Energy is needed to do it13

13 13W = Fd13

bull  W is the work done = energy used13bull  F is the force applied13bull  d is the distance through which the force acts13bull  Only the force that acts in the direction of motion counts

towards work13

1113

Okay what is Force then13bull  Force is a pushingpulling agent13bull  Examples13

ndash  gravity exerts a downward force on you13ndash  the floor exerts an upward force on a ball during its bounce13ndash  a car seat exerts a forward force on your body when you accelerate forward from

a stop13ndash  the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)13ndash  you exert a sideways force on a couch that you slide across the floor13ndash  a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your head13ndash  the expanding gas in your carrsquos cylinder exerts a force against the piston13

Forces have Direction13bull  In all the previous examples force had a

direction associated with it13bull  If multiple forces act on an object they

could potentially add or cancel depending on direction13

Force 1 Force 2

Total Force Force 1

Force 2

Total Force = 0

1213

When net force is not zero13bull  When an object experiences a non-zero net force it must

accelerate13bull  Newtonrsquos second law1313 13F = ma 13Force = mass times acceleration13

bull  The same force makes a small object accelerate more than it would a more massive object13ndash  hit a golf ball and a bowling ball with a golf club and see what

happens13

Question13A 150 lb person is standing still on the edge of a cliff What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

1313

Question13A 150 lb person jumps (or was he pushed) off a cliff and is falling to their death What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

But what is acceleration13

bull  This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellip13

bull  Acceleration is any change in velocity (speed andor direction of motion)13

bull  Measured as rate of change of velocity13ndash  velocity is expressed in meters per second (ms)13ndash  acceleration is meters per second per second13ndash  expressed as ms2 (meters per second-squared)13

1413

Putting it back together Units of Energy13

bull  Force is a mass times an acceleration (F=ma)13ndash  mass has units of kilograms13ndash  acceleration is ms213ndash  force is then kgms2 which we call Newtons (N)13

bull  Work is a force times a distance (W=Fd)13ndash  units are then (kgms2)m = kg m2s2 = Nm = Joules (J)13ndash  One joule is one Newton of force acting through one meter13ndash  Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J13bull  Energy has the same units as work Joules13

A Zoo of Units13bull  The main metric unit of energy is the Joule and most of

the world uses this but many others exist13bull  The calorie is 4184 Joules13

ndash  raise 1 gram (cc) of water one degree Celsius13bull  The Calorie (kilocalorie) is 4184 J (used for food energy) 13

ndash  raise 1 kg (1 liter) of water one degree Celsius13bull  The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one match13ndash  raise 1 pound of water one degree Fahrenheit13

bull  The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860 Calories (used for electrical energy)13ndash  one Watt (W) is one Joule per second 13ndash  a kWh is 1000 W for one hour (3600 seconds)13

bull  Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feet of natural gas gram of Uranium or amount of any energy containing source etc13

1513

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

The Physics of Energy Formula List13bull  Lots of forms of energy coming fast and furious but to put

it in perspective herersquos a list of formulas13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

1613

Kinetic Energy13bull  Kinetic Energy the energy of motion13bull  Moving things carry energy in the amount1313 13 13KE = frac12mv213

bull  Note the v2 dependencemdashthis is why13ndash  a car at 60 mph is 4 times more dangerous than a car at 30 mph13ndash  hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force winds13ndash  a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you could shoot it13

Numerical examples of kinetic energy13

bull  A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy1313 13 13KE = frac12times(0145 kg)times(30 ms)21313 13 13 13= 6525 kgm2s2 asymp 65 J = 0016 Calories13

bull  A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy is1313 13 13 KE = frac12times(000567 kg)times(5 ms)21313 13 13 13= 007 kgm2s2 = 007 J13

1713

More numerical examples13

bull  A 1500 kg car moves down the freeway at 30 ms (67 mph)1313 13 KE = frac12times(1500 kg)times(30 ms)21313 13 13 13= 675000 kgm2s2 = 675 kJ13

Convert to Calories 4184 kJ = 1 Calorie13675 kJ (1 Calorie4184 kJ) = 161 Calorie13

bull  A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)1313 13 KE = frac12times(2 kg)times(1 ms)21313 13 13 13= 1 kgm2s2 = 1 J13

Question13Kinetic energy is E = 12 m v2 Which has more energy13

A 10 kg object going 100 ms13

B 100 kg object going 10 ms13

C 1 kg object going 1000 ms13

D 1000 kg object going 1 ms13

1 ms = 22 mph13

1813

Gravitational Potential Energy13bull  It takes work to lift a mass against the pull (force) of

gravity13bull  The force of gravity is mg where m is the mass and g is

the gravitational acceleration1313 13 13F = mg 13(note similarity to F = ma)13

ndash  g = 98 ms2 on the surface of the earth or 32 fts213bull  Lifting a height h against the gravitational force

requires an energy input (work) of1313 13ΔE = W = F h = mgh13

bull  Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below13

bull  Water in river or hydroelectric plant is using potential energy that it got from being lifted up when Sun (solar energy) evaporated the water13

Question13Potential energy is E = 10 m h (metric units) Which has more energy13

A 1 ton of water at a height of 100 ft 13

B 100 tons of water at a height of 1 ft 13

C 200 lb (110 ton) of water at 1000 ft13

D All of the above have same energy13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

213

bull  Long ago almost all of our energy came from food (delivering muscle power) and almost all our energy went into securing food for ourselves13

bull  Enter the work animal supplementing our muscle power and enabling larger-scale agriculture13

bull  Next burn wood to run boilers trains13bull  150 years ago muscular effort and firewood

provided most of our energymdashand today this is less than 1 of the story13

bull  Today much more energy goes into growingharvesting food than comes out of food13

bull  Today in US 86 of our energy comes from fossil fuels (oilnatural gas coal)13

Fuzzy on the concept of energy13

bull  Donrsquot worrymdashwersquoll cover that13

313

A note on graphs log vs linear13bull  Many graphs are on logarithmic scales watch for this13bull  This condenses wide-ranging information into a compact

area13bull  Pay attention because you could warp your intuition if you

donrsquot appreciate the scale13bull  Log scales work in factors of ten13bull  A given vertical span represents a constant ratio (eg

factor of ten factor of two etc)13bull  An exponential increase looks like a straight line on a

logarithmic scale13

413

Example Plots13

Exponential plot is curved on linear scale and straight on a logarithmic scale

513

A brief history of fossil fuels13

bull  Here today gone tomorrow13bull  What will our future hold13

ndash  Will it be back to a simple life13ndash  Or will we find new ways to produce all the energy we want13ndash  Or will it be somewhere in the middle13

Global Energy Where Does it Come From13

Source131018 Joulesyr13

(~QBtuyr)13Percent of

Total13Petroleum13 15813 40013Coal13 9213 23213Natural Gas13 8913 22513Hydroelectric13 28713 7213Nuclear Energy13 2613 6613Biomass (burning)13 1613 0413Geothermal13 0513 01313Wind13 01313 00313Solar Direct13 00313 000813Sun Abs by Earth13 200000013

then radiated away13

Ultimately derived from our sun

Courtesy David Bodansky (UW)

613

713

Why do we use so much energy13

813

913

We live in a special time and placehellip13bull  We use almost 100 times the amount used by the rest of the

world (by population)13bull  This phase has only lasted for the last century or so13bull  Most of our resources come from fossil fuels presently and

this has a short finite lifetime13bull  Fossil fuels formed from solar energy over 300 million

years will be used up in a few centuries13

2000 2500 3000 3500 4000 1500 1000 500 0

year

ener

gy u

sage

1013

Energy the capacity to do work13

bull  This notion makes sense even in a colloquial context13ndash  hard to get work done when yoursquore wiped out

(low on energy)13ndash work makes you tired yoursquove used up energy13

bull  But we can make this definition of energy much more precise by specifying exactly what we mean by work13

Work =Energy more than just unpleasant tasks13

bull  In physics the definition of work is the application of a force through a distance Energy is needed to do it13

13 13W = Fd13

bull  W is the work done = energy used13bull  F is the force applied13bull  d is the distance through which the force acts13bull  Only the force that acts in the direction of motion counts

towards work13

1113

Okay what is Force then13bull  Force is a pushingpulling agent13bull  Examples13

ndash  gravity exerts a downward force on you13ndash  the floor exerts an upward force on a ball during its bounce13ndash  a car seat exerts a forward force on your body when you accelerate forward from

a stop13ndash  the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)13ndash  you exert a sideways force on a couch that you slide across the floor13ndash  a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your head13ndash  the expanding gas in your carrsquos cylinder exerts a force against the piston13

Forces have Direction13bull  In all the previous examples force had a

direction associated with it13bull  If multiple forces act on an object they

could potentially add or cancel depending on direction13

Force 1 Force 2

Total Force Force 1

Force 2

Total Force = 0

1213

When net force is not zero13bull  When an object experiences a non-zero net force it must

accelerate13bull  Newtonrsquos second law1313 13F = ma 13Force = mass times acceleration13

bull  The same force makes a small object accelerate more than it would a more massive object13ndash  hit a golf ball and a bowling ball with a golf club and see what

happens13

Question13A 150 lb person is standing still on the edge of a cliff What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

1313

Question13A 150 lb person jumps (or was he pushed) off a cliff and is falling to their death What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

But what is acceleration13

bull  This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellip13

bull  Acceleration is any change in velocity (speed andor direction of motion)13

bull  Measured as rate of change of velocity13ndash  velocity is expressed in meters per second (ms)13ndash  acceleration is meters per second per second13ndash  expressed as ms2 (meters per second-squared)13

1413

Putting it back together Units of Energy13

bull  Force is a mass times an acceleration (F=ma)13ndash  mass has units of kilograms13ndash  acceleration is ms213ndash  force is then kgms2 which we call Newtons (N)13

bull  Work is a force times a distance (W=Fd)13ndash  units are then (kgms2)m = kg m2s2 = Nm = Joules (J)13ndash  One joule is one Newton of force acting through one meter13ndash  Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J13bull  Energy has the same units as work Joules13

A Zoo of Units13bull  The main metric unit of energy is the Joule and most of

the world uses this but many others exist13bull  The calorie is 4184 Joules13

ndash  raise 1 gram (cc) of water one degree Celsius13bull  The Calorie (kilocalorie) is 4184 J (used for food energy) 13

ndash  raise 1 kg (1 liter) of water one degree Celsius13bull  The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one match13ndash  raise 1 pound of water one degree Fahrenheit13

bull  The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860 Calories (used for electrical energy)13ndash  one Watt (W) is one Joule per second 13ndash  a kWh is 1000 W for one hour (3600 seconds)13

bull  Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feet of natural gas gram of Uranium or amount of any energy containing source etc13

1513

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

The Physics of Energy Formula List13bull  Lots of forms of energy coming fast and furious but to put

it in perspective herersquos a list of formulas13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

1613

Kinetic Energy13bull  Kinetic Energy the energy of motion13bull  Moving things carry energy in the amount1313 13 13KE = frac12mv213

bull  Note the v2 dependencemdashthis is why13ndash  a car at 60 mph is 4 times more dangerous than a car at 30 mph13ndash  hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force winds13ndash  a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you could shoot it13

Numerical examples of kinetic energy13

bull  A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy1313 13 13KE = frac12times(0145 kg)times(30 ms)21313 13 13 13= 6525 kgm2s2 asymp 65 J = 0016 Calories13

bull  A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy is1313 13 13 KE = frac12times(000567 kg)times(5 ms)21313 13 13 13= 007 kgm2s2 = 007 J13

1713

More numerical examples13

bull  A 1500 kg car moves down the freeway at 30 ms (67 mph)1313 13 KE = frac12times(1500 kg)times(30 ms)21313 13 13 13= 675000 kgm2s2 = 675 kJ13

Convert to Calories 4184 kJ = 1 Calorie13675 kJ (1 Calorie4184 kJ) = 161 Calorie13

bull  A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)1313 13 KE = frac12times(2 kg)times(1 ms)21313 13 13 13= 1 kgm2s2 = 1 J13

Question13Kinetic energy is E = 12 m v2 Which has more energy13

A 10 kg object going 100 ms13

B 100 kg object going 10 ms13

C 1 kg object going 1000 ms13

D 1000 kg object going 1 ms13

1 ms = 22 mph13

1813

Gravitational Potential Energy13bull  It takes work to lift a mass against the pull (force) of

gravity13bull  The force of gravity is mg where m is the mass and g is

the gravitational acceleration1313 13 13F = mg 13(note similarity to F = ma)13

ndash  g = 98 ms2 on the surface of the earth or 32 fts213bull  Lifting a height h against the gravitational force

requires an energy input (work) of1313 13ΔE = W = F h = mgh13

bull  Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below13

bull  Water in river or hydroelectric plant is using potential energy that it got from being lifted up when Sun (solar energy) evaporated the water13

Question13Potential energy is E = 10 m h (metric units) Which has more energy13

A 1 ton of water at a height of 100 ft 13

B 100 tons of water at a height of 1 ft 13

C 200 lb (110 ton) of water at 1000 ft13

D All of the above have same energy13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

313

A note on graphs log vs linear13bull  Many graphs are on logarithmic scales watch for this13bull  This condenses wide-ranging information into a compact

area13bull  Pay attention because you could warp your intuition if you

donrsquot appreciate the scale13bull  Log scales work in factors of ten13bull  A given vertical span represents a constant ratio (eg

factor of ten factor of two etc)13bull  An exponential increase looks like a straight line on a

logarithmic scale13

413

Example Plots13

Exponential plot is curved on linear scale and straight on a logarithmic scale

513

A brief history of fossil fuels13

bull  Here today gone tomorrow13bull  What will our future hold13

ndash  Will it be back to a simple life13ndash  Or will we find new ways to produce all the energy we want13ndash  Or will it be somewhere in the middle13

Global Energy Where Does it Come From13

Source131018 Joulesyr13

(~QBtuyr)13Percent of

Total13Petroleum13 15813 40013Coal13 9213 23213Natural Gas13 8913 22513Hydroelectric13 28713 7213Nuclear Energy13 2613 6613Biomass (burning)13 1613 0413Geothermal13 0513 01313Wind13 01313 00313Solar Direct13 00313 000813Sun Abs by Earth13 200000013

then radiated away13

Ultimately derived from our sun

Courtesy David Bodansky (UW)

613

713

Why do we use so much energy13

813

913

We live in a special time and placehellip13bull  We use almost 100 times the amount used by the rest of the

world (by population)13bull  This phase has only lasted for the last century or so13bull  Most of our resources come from fossil fuels presently and

this has a short finite lifetime13bull  Fossil fuels formed from solar energy over 300 million

years will be used up in a few centuries13

2000 2500 3000 3500 4000 1500 1000 500 0

year

ener

gy u

sage

1013

Energy the capacity to do work13

bull  This notion makes sense even in a colloquial context13ndash  hard to get work done when yoursquore wiped out

(low on energy)13ndash work makes you tired yoursquove used up energy13

bull  But we can make this definition of energy much more precise by specifying exactly what we mean by work13

Work =Energy more than just unpleasant tasks13

bull  In physics the definition of work is the application of a force through a distance Energy is needed to do it13

13 13W = Fd13

bull  W is the work done = energy used13bull  F is the force applied13bull  d is the distance through which the force acts13bull  Only the force that acts in the direction of motion counts

towards work13

1113

Okay what is Force then13bull  Force is a pushingpulling agent13bull  Examples13

ndash  gravity exerts a downward force on you13ndash  the floor exerts an upward force on a ball during its bounce13ndash  a car seat exerts a forward force on your body when you accelerate forward from

a stop13ndash  the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)13ndash  you exert a sideways force on a couch that you slide across the floor13ndash  a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your head13ndash  the expanding gas in your carrsquos cylinder exerts a force against the piston13

Forces have Direction13bull  In all the previous examples force had a

direction associated with it13bull  If multiple forces act on an object they

could potentially add or cancel depending on direction13

Force 1 Force 2

Total Force Force 1

Force 2

Total Force = 0

1213

When net force is not zero13bull  When an object experiences a non-zero net force it must

accelerate13bull  Newtonrsquos second law1313 13F = ma 13Force = mass times acceleration13

bull  The same force makes a small object accelerate more than it would a more massive object13ndash  hit a golf ball and a bowling ball with a golf club and see what

happens13

Question13A 150 lb person is standing still on the edge of a cliff What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

1313

Question13A 150 lb person jumps (or was he pushed) off a cliff and is falling to their death What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

But what is acceleration13

bull  This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellip13

bull  Acceleration is any change in velocity (speed andor direction of motion)13

bull  Measured as rate of change of velocity13ndash  velocity is expressed in meters per second (ms)13ndash  acceleration is meters per second per second13ndash  expressed as ms2 (meters per second-squared)13

1413

Putting it back together Units of Energy13

bull  Force is a mass times an acceleration (F=ma)13ndash  mass has units of kilograms13ndash  acceleration is ms213ndash  force is then kgms2 which we call Newtons (N)13

bull  Work is a force times a distance (W=Fd)13ndash  units are then (kgms2)m = kg m2s2 = Nm = Joules (J)13ndash  One joule is one Newton of force acting through one meter13ndash  Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J13bull  Energy has the same units as work Joules13

A Zoo of Units13bull  The main metric unit of energy is the Joule and most of

the world uses this but many others exist13bull  The calorie is 4184 Joules13

ndash  raise 1 gram (cc) of water one degree Celsius13bull  The Calorie (kilocalorie) is 4184 J (used for food energy) 13

ndash  raise 1 kg (1 liter) of water one degree Celsius13bull  The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one match13ndash  raise 1 pound of water one degree Fahrenheit13

bull  The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860 Calories (used for electrical energy)13ndash  one Watt (W) is one Joule per second 13ndash  a kWh is 1000 W for one hour (3600 seconds)13

bull  Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feet of natural gas gram of Uranium or amount of any energy containing source etc13

1513

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

The Physics of Energy Formula List13bull  Lots of forms of energy coming fast and furious but to put

it in perspective herersquos a list of formulas13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

1613

Kinetic Energy13bull  Kinetic Energy the energy of motion13bull  Moving things carry energy in the amount1313 13 13KE = frac12mv213

bull  Note the v2 dependencemdashthis is why13ndash  a car at 60 mph is 4 times more dangerous than a car at 30 mph13ndash  hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force winds13ndash  a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you could shoot it13

Numerical examples of kinetic energy13

bull  A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy1313 13 13KE = frac12times(0145 kg)times(30 ms)21313 13 13 13= 6525 kgm2s2 asymp 65 J = 0016 Calories13

bull  A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy is1313 13 13 KE = frac12times(000567 kg)times(5 ms)21313 13 13 13= 007 kgm2s2 = 007 J13

1713

More numerical examples13

bull  A 1500 kg car moves down the freeway at 30 ms (67 mph)1313 13 KE = frac12times(1500 kg)times(30 ms)21313 13 13 13= 675000 kgm2s2 = 675 kJ13

Convert to Calories 4184 kJ = 1 Calorie13675 kJ (1 Calorie4184 kJ) = 161 Calorie13

bull  A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)1313 13 KE = frac12times(2 kg)times(1 ms)21313 13 13 13= 1 kgm2s2 = 1 J13

Question13Kinetic energy is E = 12 m v2 Which has more energy13

A 10 kg object going 100 ms13

B 100 kg object going 10 ms13

C 1 kg object going 1000 ms13

D 1000 kg object going 1 ms13

1 ms = 22 mph13

1813

Gravitational Potential Energy13bull  It takes work to lift a mass against the pull (force) of

gravity13bull  The force of gravity is mg where m is the mass and g is

the gravitational acceleration1313 13 13F = mg 13(note similarity to F = ma)13

ndash  g = 98 ms2 on the surface of the earth or 32 fts213bull  Lifting a height h against the gravitational force

requires an energy input (work) of1313 13ΔE = W = F h = mgh13

bull  Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below13

bull  Water in river or hydroelectric plant is using potential energy that it got from being lifted up when Sun (solar energy) evaporated the water13

Question13Potential energy is E = 10 m h (metric units) Which has more energy13

A 1 ton of water at a height of 100 ft 13

B 100 tons of water at a height of 1 ft 13

C 200 lb (110 ton) of water at 1000 ft13

D All of the above have same energy13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

413

Example Plots13

Exponential plot is curved on linear scale and straight on a logarithmic scale

513

A brief history of fossil fuels13

bull  Here today gone tomorrow13bull  What will our future hold13

ndash  Will it be back to a simple life13ndash  Or will we find new ways to produce all the energy we want13ndash  Or will it be somewhere in the middle13

Global Energy Where Does it Come From13

Source131018 Joulesyr13

(~QBtuyr)13Percent of

Total13Petroleum13 15813 40013Coal13 9213 23213Natural Gas13 8913 22513Hydroelectric13 28713 7213Nuclear Energy13 2613 6613Biomass (burning)13 1613 0413Geothermal13 0513 01313Wind13 01313 00313Solar Direct13 00313 000813Sun Abs by Earth13 200000013

then radiated away13

Ultimately derived from our sun

Courtesy David Bodansky (UW)

613

713

Why do we use so much energy13

813

913

We live in a special time and placehellip13bull  We use almost 100 times the amount used by the rest of the

world (by population)13bull  This phase has only lasted for the last century or so13bull  Most of our resources come from fossil fuels presently and

this has a short finite lifetime13bull  Fossil fuels formed from solar energy over 300 million

years will be used up in a few centuries13

2000 2500 3000 3500 4000 1500 1000 500 0

year

ener

gy u

sage

1013

Energy the capacity to do work13

bull  This notion makes sense even in a colloquial context13ndash  hard to get work done when yoursquore wiped out

(low on energy)13ndash work makes you tired yoursquove used up energy13

bull  But we can make this definition of energy much more precise by specifying exactly what we mean by work13

Work =Energy more than just unpleasant tasks13

bull  In physics the definition of work is the application of a force through a distance Energy is needed to do it13

13 13W = Fd13

bull  W is the work done = energy used13bull  F is the force applied13bull  d is the distance through which the force acts13bull  Only the force that acts in the direction of motion counts

towards work13

1113

Okay what is Force then13bull  Force is a pushingpulling agent13bull  Examples13

ndash  gravity exerts a downward force on you13ndash  the floor exerts an upward force on a ball during its bounce13ndash  a car seat exerts a forward force on your body when you accelerate forward from

a stop13ndash  the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)13ndash  you exert a sideways force on a couch that you slide across the floor13ndash  a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your head13ndash  the expanding gas in your carrsquos cylinder exerts a force against the piston13

Forces have Direction13bull  In all the previous examples force had a

direction associated with it13bull  If multiple forces act on an object they

could potentially add or cancel depending on direction13

Force 1 Force 2

Total Force Force 1

Force 2

Total Force = 0

1213

When net force is not zero13bull  When an object experiences a non-zero net force it must

accelerate13bull  Newtonrsquos second law1313 13F = ma 13Force = mass times acceleration13

bull  The same force makes a small object accelerate more than it would a more massive object13ndash  hit a golf ball and a bowling ball with a golf club and see what

happens13

Question13A 150 lb person is standing still on the edge of a cliff What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

1313

Question13A 150 lb person jumps (or was he pushed) off a cliff and is falling to their death What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

But what is acceleration13

bull  This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellip13

bull  Acceleration is any change in velocity (speed andor direction of motion)13

bull  Measured as rate of change of velocity13ndash  velocity is expressed in meters per second (ms)13ndash  acceleration is meters per second per second13ndash  expressed as ms2 (meters per second-squared)13

1413

Putting it back together Units of Energy13

bull  Force is a mass times an acceleration (F=ma)13ndash  mass has units of kilograms13ndash  acceleration is ms213ndash  force is then kgms2 which we call Newtons (N)13

bull  Work is a force times a distance (W=Fd)13ndash  units are then (kgms2)m = kg m2s2 = Nm = Joules (J)13ndash  One joule is one Newton of force acting through one meter13ndash  Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J13bull  Energy has the same units as work Joules13

A Zoo of Units13bull  The main metric unit of energy is the Joule and most of

the world uses this but many others exist13bull  The calorie is 4184 Joules13

ndash  raise 1 gram (cc) of water one degree Celsius13bull  The Calorie (kilocalorie) is 4184 J (used for food energy) 13

ndash  raise 1 kg (1 liter) of water one degree Celsius13bull  The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one match13ndash  raise 1 pound of water one degree Fahrenheit13

bull  The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860 Calories (used for electrical energy)13ndash  one Watt (W) is one Joule per second 13ndash  a kWh is 1000 W for one hour (3600 seconds)13

bull  Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feet of natural gas gram of Uranium or amount of any energy containing source etc13

1513

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

The Physics of Energy Formula List13bull  Lots of forms of energy coming fast and furious but to put

it in perspective herersquos a list of formulas13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

1613

Kinetic Energy13bull  Kinetic Energy the energy of motion13bull  Moving things carry energy in the amount1313 13 13KE = frac12mv213

bull  Note the v2 dependencemdashthis is why13ndash  a car at 60 mph is 4 times more dangerous than a car at 30 mph13ndash  hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force winds13ndash  a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you could shoot it13

Numerical examples of kinetic energy13

bull  A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy1313 13 13KE = frac12times(0145 kg)times(30 ms)21313 13 13 13= 6525 kgm2s2 asymp 65 J = 0016 Calories13

bull  A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy is1313 13 13 KE = frac12times(000567 kg)times(5 ms)21313 13 13 13= 007 kgm2s2 = 007 J13

1713

More numerical examples13

bull  A 1500 kg car moves down the freeway at 30 ms (67 mph)1313 13 KE = frac12times(1500 kg)times(30 ms)21313 13 13 13= 675000 kgm2s2 = 675 kJ13

Convert to Calories 4184 kJ = 1 Calorie13675 kJ (1 Calorie4184 kJ) = 161 Calorie13

bull  A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)1313 13 KE = frac12times(2 kg)times(1 ms)21313 13 13 13= 1 kgm2s2 = 1 J13

Question13Kinetic energy is E = 12 m v2 Which has more energy13

A 10 kg object going 100 ms13

B 100 kg object going 10 ms13

C 1 kg object going 1000 ms13

D 1000 kg object going 1 ms13

1 ms = 22 mph13

1813

Gravitational Potential Energy13bull  It takes work to lift a mass against the pull (force) of

gravity13bull  The force of gravity is mg where m is the mass and g is

the gravitational acceleration1313 13 13F = mg 13(note similarity to F = ma)13

ndash  g = 98 ms2 on the surface of the earth or 32 fts213bull  Lifting a height h against the gravitational force

requires an energy input (work) of1313 13ΔE = W = F h = mgh13

bull  Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below13

bull  Water in river or hydroelectric plant is using potential energy that it got from being lifted up when Sun (solar energy) evaporated the water13

Question13Potential energy is E = 10 m h (metric units) Which has more energy13

A 1 ton of water at a height of 100 ft 13

B 100 tons of water at a height of 1 ft 13

C 200 lb (110 ton) of water at 1000 ft13

D All of the above have same energy13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

513

A brief history of fossil fuels13

bull  Here today gone tomorrow13bull  What will our future hold13

ndash  Will it be back to a simple life13ndash  Or will we find new ways to produce all the energy we want13ndash  Or will it be somewhere in the middle13

Global Energy Where Does it Come From13

Source131018 Joulesyr13

(~QBtuyr)13Percent of

Total13Petroleum13 15813 40013Coal13 9213 23213Natural Gas13 8913 22513Hydroelectric13 28713 7213Nuclear Energy13 2613 6613Biomass (burning)13 1613 0413Geothermal13 0513 01313Wind13 01313 00313Solar Direct13 00313 000813Sun Abs by Earth13 200000013

then radiated away13

Ultimately derived from our sun

Courtesy David Bodansky (UW)

613

713

Why do we use so much energy13

813

913

We live in a special time and placehellip13bull  We use almost 100 times the amount used by the rest of the

world (by population)13bull  This phase has only lasted for the last century or so13bull  Most of our resources come from fossil fuels presently and

this has a short finite lifetime13bull  Fossil fuels formed from solar energy over 300 million

years will be used up in a few centuries13

2000 2500 3000 3500 4000 1500 1000 500 0

year

ener

gy u

sage

1013

Energy the capacity to do work13

bull  This notion makes sense even in a colloquial context13ndash  hard to get work done when yoursquore wiped out

(low on energy)13ndash work makes you tired yoursquove used up energy13

bull  But we can make this definition of energy much more precise by specifying exactly what we mean by work13

Work =Energy more than just unpleasant tasks13

bull  In physics the definition of work is the application of a force through a distance Energy is needed to do it13

13 13W = Fd13

bull  W is the work done = energy used13bull  F is the force applied13bull  d is the distance through which the force acts13bull  Only the force that acts in the direction of motion counts

towards work13

1113

Okay what is Force then13bull  Force is a pushingpulling agent13bull  Examples13

ndash  gravity exerts a downward force on you13ndash  the floor exerts an upward force on a ball during its bounce13ndash  a car seat exerts a forward force on your body when you accelerate forward from

a stop13ndash  the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)13ndash  you exert a sideways force on a couch that you slide across the floor13ndash  a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your head13ndash  the expanding gas in your carrsquos cylinder exerts a force against the piston13

Forces have Direction13bull  In all the previous examples force had a

direction associated with it13bull  If multiple forces act on an object they

could potentially add or cancel depending on direction13

Force 1 Force 2

Total Force Force 1

Force 2

Total Force = 0

1213

When net force is not zero13bull  When an object experiences a non-zero net force it must

accelerate13bull  Newtonrsquos second law1313 13F = ma 13Force = mass times acceleration13

bull  The same force makes a small object accelerate more than it would a more massive object13ndash  hit a golf ball and a bowling ball with a golf club and see what

happens13

Question13A 150 lb person is standing still on the edge of a cliff What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

1313

Question13A 150 lb person jumps (or was he pushed) off a cliff and is falling to their death What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

But what is acceleration13

bull  This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellip13

bull  Acceleration is any change in velocity (speed andor direction of motion)13

bull  Measured as rate of change of velocity13ndash  velocity is expressed in meters per second (ms)13ndash  acceleration is meters per second per second13ndash  expressed as ms2 (meters per second-squared)13

1413

Putting it back together Units of Energy13

bull  Force is a mass times an acceleration (F=ma)13ndash  mass has units of kilograms13ndash  acceleration is ms213ndash  force is then kgms2 which we call Newtons (N)13

bull  Work is a force times a distance (W=Fd)13ndash  units are then (kgms2)m = kg m2s2 = Nm = Joules (J)13ndash  One joule is one Newton of force acting through one meter13ndash  Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J13bull  Energy has the same units as work Joules13

A Zoo of Units13bull  The main metric unit of energy is the Joule and most of

the world uses this but many others exist13bull  The calorie is 4184 Joules13

ndash  raise 1 gram (cc) of water one degree Celsius13bull  The Calorie (kilocalorie) is 4184 J (used for food energy) 13

ndash  raise 1 kg (1 liter) of water one degree Celsius13bull  The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one match13ndash  raise 1 pound of water one degree Fahrenheit13

bull  The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860 Calories (used for electrical energy)13ndash  one Watt (W) is one Joule per second 13ndash  a kWh is 1000 W for one hour (3600 seconds)13

bull  Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feet of natural gas gram of Uranium or amount of any energy containing source etc13

1513

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

The Physics of Energy Formula List13bull  Lots of forms of energy coming fast and furious but to put

it in perspective herersquos a list of formulas13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

1613

Kinetic Energy13bull  Kinetic Energy the energy of motion13bull  Moving things carry energy in the amount1313 13 13KE = frac12mv213

bull  Note the v2 dependencemdashthis is why13ndash  a car at 60 mph is 4 times more dangerous than a car at 30 mph13ndash  hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force winds13ndash  a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you could shoot it13

Numerical examples of kinetic energy13

bull  A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy1313 13 13KE = frac12times(0145 kg)times(30 ms)21313 13 13 13= 6525 kgm2s2 asymp 65 J = 0016 Calories13

bull  A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy is1313 13 13 KE = frac12times(000567 kg)times(5 ms)21313 13 13 13= 007 kgm2s2 = 007 J13

1713

More numerical examples13

bull  A 1500 kg car moves down the freeway at 30 ms (67 mph)1313 13 KE = frac12times(1500 kg)times(30 ms)21313 13 13 13= 675000 kgm2s2 = 675 kJ13

Convert to Calories 4184 kJ = 1 Calorie13675 kJ (1 Calorie4184 kJ) = 161 Calorie13

bull  A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)1313 13 KE = frac12times(2 kg)times(1 ms)21313 13 13 13= 1 kgm2s2 = 1 J13

Question13Kinetic energy is E = 12 m v2 Which has more energy13

A 10 kg object going 100 ms13

B 100 kg object going 10 ms13

C 1 kg object going 1000 ms13

D 1000 kg object going 1 ms13

1 ms = 22 mph13

1813

Gravitational Potential Energy13bull  It takes work to lift a mass against the pull (force) of

gravity13bull  The force of gravity is mg where m is the mass and g is

the gravitational acceleration1313 13 13F = mg 13(note similarity to F = ma)13

ndash  g = 98 ms2 on the surface of the earth or 32 fts213bull  Lifting a height h against the gravitational force

requires an energy input (work) of1313 13ΔE = W = F h = mgh13

bull  Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below13

bull  Water in river or hydroelectric plant is using potential energy that it got from being lifted up when Sun (solar energy) evaporated the water13

Question13Potential energy is E = 10 m h (metric units) Which has more energy13

A 1 ton of water at a height of 100 ft 13

B 100 tons of water at a height of 1 ft 13

C 200 lb (110 ton) of water at 1000 ft13

D All of the above have same energy13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

613

713

Why do we use so much energy13

813

913

We live in a special time and placehellip13bull  We use almost 100 times the amount used by the rest of the

world (by population)13bull  This phase has only lasted for the last century or so13bull  Most of our resources come from fossil fuels presently and

this has a short finite lifetime13bull  Fossil fuels formed from solar energy over 300 million

years will be used up in a few centuries13

2000 2500 3000 3500 4000 1500 1000 500 0

year

ener

gy u

sage

1013

Energy the capacity to do work13

bull  This notion makes sense even in a colloquial context13ndash  hard to get work done when yoursquore wiped out

(low on energy)13ndash work makes you tired yoursquove used up energy13

bull  But we can make this definition of energy much more precise by specifying exactly what we mean by work13

Work =Energy more than just unpleasant tasks13

bull  In physics the definition of work is the application of a force through a distance Energy is needed to do it13

13 13W = Fd13

bull  W is the work done = energy used13bull  F is the force applied13bull  d is the distance through which the force acts13bull  Only the force that acts in the direction of motion counts

towards work13

1113

Okay what is Force then13bull  Force is a pushingpulling agent13bull  Examples13

ndash  gravity exerts a downward force on you13ndash  the floor exerts an upward force on a ball during its bounce13ndash  a car seat exerts a forward force on your body when you accelerate forward from

a stop13ndash  the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)13ndash  you exert a sideways force on a couch that you slide across the floor13ndash  a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your head13ndash  the expanding gas in your carrsquos cylinder exerts a force against the piston13

Forces have Direction13bull  In all the previous examples force had a

direction associated with it13bull  If multiple forces act on an object they

could potentially add or cancel depending on direction13

Force 1 Force 2

Total Force Force 1

Force 2

Total Force = 0

1213

When net force is not zero13bull  When an object experiences a non-zero net force it must

accelerate13bull  Newtonrsquos second law1313 13F = ma 13Force = mass times acceleration13

bull  The same force makes a small object accelerate more than it would a more massive object13ndash  hit a golf ball and a bowling ball with a golf club and see what

happens13

Question13A 150 lb person is standing still on the edge of a cliff What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

1313

Question13A 150 lb person jumps (or was he pushed) off a cliff and is falling to their death What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

But what is acceleration13

bull  This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellip13

bull  Acceleration is any change in velocity (speed andor direction of motion)13

bull  Measured as rate of change of velocity13ndash  velocity is expressed in meters per second (ms)13ndash  acceleration is meters per second per second13ndash  expressed as ms2 (meters per second-squared)13

1413

Putting it back together Units of Energy13

bull  Force is a mass times an acceleration (F=ma)13ndash  mass has units of kilograms13ndash  acceleration is ms213ndash  force is then kgms2 which we call Newtons (N)13

bull  Work is a force times a distance (W=Fd)13ndash  units are then (kgms2)m = kg m2s2 = Nm = Joules (J)13ndash  One joule is one Newton of force acting through one meter13ndash  Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J13bull  Energy has the same units as work Joules13

A Zoo of Units13bull  The main metric unit of energy is the Joule and most of

the world uses this but many others exist13bull  The calorie is 4184 Joules13

ndash  raise 1 gram (cc) of water one degree Celsius13bull  The Calorie (kilocalorie) is 4184 J (used for food energy) 13

ndash  raise 1 kg (1 liter) of water one degree Celsius13bull  The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one match13ndash  raise 1 pound of water one degree Fahrenheit13

bull  The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860 Calories (used for electrical energy)13ndash  one Watt (W) is one Joule per second 13ndash  a kWh is 1000 W for one hour (3600 seconds)13

bull  Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feet of natural gas gram of Uranium or amount of any energy containing source etc13

1513

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

The Physics of Energy Formula List13bull  Lots of forms of energy coming fast and furious but to put

it in perspective herersquos a list of formulas13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

1613

Kinetic Energy13bull  Kinetic Energy the energy of motion13bull  Moving things carry energy in the amount1313 13 13KE = frac12mv213

bull  Note the v2 dependencemdashthis is why13ndash  a car at 60 mph is 4 times more dangerous than a car at 30 mph13ndash  hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force winds13ndash  a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you could shoot it13

Numerical examples of kinetic energy13

bull  A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy1313 13 13KE = frac12times(0145 kg)times(30 ms)21313 13 13 13= 6525 kgm2s2 asymp 65 J = 0016 Calories13

bull  A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy is1313 13 13 KE = frac12times(000567 kg)times(5 ms)21313 13 13 13= 007 kgm2s2 = 007 J13

1713

More numerical examples13

bull  A 1500 kg car moves down the freeway at 30 ms (67 mph)1313 13 KE = frac12times(1500 kg)times(30 ms)21313 13 13 13= 675000 kgm2s2 = 675 kJ13

Convert to Calories 4184 kJ = 1 Calorie13675 kJ (1 Calorie4184 kJ) = 161 Calorie13

bull  A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)1313 13 KE = frac12times(2 kg)times(1 ms)21313 13 13 13= 1 kgm2s2 = 1 J13

Question13Kinetic energy is E = 12 m v2 Which has more energy13

A 10 kg object going 100 ms13

B 100 kg object going 10 ms13

C 1 kg object going 1000 ms13

D 1000 kg object going 1 ms13

1 ms = 22 mph13

1813

Gravitational Potential Energy13bull  It takes work to lift a mass against the pull (force) of

gravity13bull  The force of gravity is mg where m is the mass and g is

the gravitational acceleration1313 13 13F = mg 13(note similarity to F = ma)13

ndash  g = 98 ms2 on the surface of the earth or 32 fts213bull  Lifting a height h against the gravitational force

requires an energy input (work) of1313 13ΔE = W = F h = mgh13

bull  Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below13

bull  Water in river or hydroelectric plant is using potential energy that it got from being lifted up when Sun (solar energy) evaporated the water13

Question13Potential energy is E = 10 m h (metric units) Which has more energy13

A 1 ton of water at a height of 100 ft 13

B 100 tons of water at a height of 1 ft 13

C 200 lb (110 ton) of water at 1000 ft13

D All of the above have same energy13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

713

Why do we use so much energy13

813

913

We live in a special time and placehellip13bull  We use almost 100 times the amount used by the rest of the

world (by population)13bull  This phase has only lasted for the last century or so13bull  Most of our resources come from fossil fuels presently and

this has a short finite lifetime13bull  Fossil fuels formed from solar energy over 300 million

years will be used up in a few centuries13

2000 2500 3000 3500 4000 1500 1000 500 0

year

ener

gy u

sage

1013

Energy the capacity to do work13

bull  This notion makes sense even in a colloquial context13ndash  hard to get work done when yoursquore wiped out

(low on energy)13ndash work makes you tired yoursquove used up energy13

bull  But we can make this definition of energy much more precise by specifying exactly what we mean by work13

Work =Energy more than just unpleasant tasks13

bull  In physics the definition of work is the application of a force through a distance Energy is needed to do it13

13 13W = Fd13

bull  W is the work done = energy used13bull  F is the force applied13bull  d is the distance through which the force acts13bull  Only the force that acts in the direction of motion counts

towards work13

1113

Okay what is Force then13bull  Force is a pushingpulling agent13bull  Examples13

ndash  gravity exerts a downward force on you13ndash  the floor exerts an upward force on a ball during its bounce13ndash  a car seat exerts a forward force on your body when you accelerate forward from

a stop13ndash  the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)13ndash  you exert a sideways force on a couch that you slide across the floor13ndash  a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your head13ndash  the expanding gas in your carrsquos cylinder exerts a force against the piston13

Forces have Direction13bull  In all the previous examples force had a

direction associated with it13bull  If multiple forces act on an object they

could potentially add or cancel depending on direction13

Force 1 Force 2

Total Force Force 1

Force 2

Total Force = 0

1213

When net force is not zero13bull  When an object experiences a non-zero net force it must

accelerate13bull  Newtonrsquos second law1313 13F = ma 13Force = mass times acceleration13

bull  The same force makes a small object accelerate more than it would a more massive object13ndash  hit a golf ball and a bowling ball with a golf club and see what

happens13

Question13A 150 lb person is standing still on the edge of a cliff What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

1313

Question13A 150 lb person jumps (or was he pushed) off a cliff and is falling to their death What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

But what is acceleration13

bull  This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellip13

bull  Acceleration is any change in velocity (speed andor direction of motion)13

bull  Measured as rate of change of velocity13ndash  velocity is expressed in meters per second (ms)13ndash  acceleration is meters per second per second13ndash  expressed as ms2 (meters per second-squared)13

1413

Putting it back together Units of Energy13

bull  Force is a mass times an acceleration (F=ma)13ndash  mass has units of kilograms13ndash  acceleration is ms213ndash  force is then kgms2 which we call Newtons (N)13

bull  Work is a force times a distance (W=Fd)13ndash  units are then (kgms2)m = kg m2s2 = Nm = Joules (J)13ndash  One joule is one Newton of force acting through one meter13ndash  Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J13bull  Energy has the same units as work Joules13

A Zoo of Units13bull  The main metric unit of energy is the Joule and most of

the world uses this but many others exist13bull  The calorie is 4184 Joules13

ndash  raise 1 gram (cc) of water one degree Celsius13bull  The Calorie (kilocalorie) is 4184 J (used for food energy) 13

ndash  raise 1 kg (1 liter) of water one degree Celsius13bull  The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one match13ndash  raise 1 pound of water one degree Fahrenheit13

bull  The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860 Calories (used for electrical energy)13ndash  one Watt (W) is one Joule per second 13ndash  a kWh is 1000 W for one hour (3600 seconds)13

bull  Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feet of natural gas gram of Uranium or amount of any energy containing source etc13

1513

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

The Physics of Energy Formula List13bull  Lots of forms of energy coming fast and furious but to put

it in perspective herersquos a list of formulas13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

1613

Kinetic Energy13bull  Kinetic Energy the energy of motion13bull  Moving things carry energy in the amount1313 13 13KE = frac12mv213

bull  Note the v2 dependencemdashthis is why13ndash  a car at 60 mph is 4 times more dangerous than a car at 30 mph13ndash  hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force winds13ndash  a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you could shoot it13

Numerical examples of kinetic energy13

bull  A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy1313 13 13KE = frac12times(0145 kg)times(30 ms)21313 13 13 13= 6525 kgm2s2 asymp 65 J = 0016 Calories13

bull  A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy is1313 13 13 KE = frac12times(000567 kg)times(5 ms)21313 13 13 13= 007 kgm2s2 = 007 J13

1713

More numerical examples13

bull  A 1500 kg car moves down the freeway at 30 ms (67 mph)1313 13 KE = frac12times(1500 kg)times(30 ms)21313 13 13 13= 675000 kgm2s2 = 675 kJ13

Convert to Calories 4184 kJ = 1 Calorie13675 kJ (1 Calorie4184 kJ) = 161 Calorie13

bull  A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)1313 13 KE = frac12times(2 kg)times(1 ms)21313 13 13 13= 1 kgm2s2 = 1 J13

Question13Kinetic energy is E = 12 m v2 Which has more energy13

A 10 kg object going 100 ms13

B 100 kg object going 10 ms13

C 1 kg object going 1000 ms13

D 1000 kg object going 1 ms13

1 ms = 22 mph13

1813

Gravitational Potential Energy13bull  It takes work to lift a mass against the pull (force) of

gravity13bull  The force of gravity is mg where m is the mass and g is

the gravitational acceleration1313 13 13F = mg 13(note similarity to F = ma)13

ndash  g = 98 ms2 on the surface of the earth or 32 fts213bull  Lifting a height h against the gravitational force

requires an energy input (work) of1313 13ΔE = W = F h = mgh13

bull  Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below13

bull  Water in river or hydroelectric plant is using potential energy that it got from being lifted up when Sun (solar energy) evaporated the water13

Question13Potential energy is E = 10 m h (metric units) Which has more energy13

A 1 ton of water at a height of 100 ft 13

B 100 tons of water at a height of 1 ft 13

C 200 lb (110 ton) of water at 1000 ft13

D All of the above have same energy13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

813

913

We live in a special time and placehellip13bull  We use almost 100 times the amount used by the rest of the

world (by population)13bull  This phase has only lasted for the last century or so13bull  Most of our resources come from fossil fuels presently and

this has a short finite lifetime13bull  Fossil fuels formed from solar energy over 300 million

years will be used up in a few centuries13

2000 2500 3000 3500 4000 1500 1000 500 0

year

ener

gy u

sage

1013

Energy the capacity to do work13

bull  This notion makes sense even in a colloquial context13ndash  hard to get work done when yoursquore wiped out

(low on energy)13ndash work makes you tired yoursquove used up energy13

bull  But we can make this definition of energy much more precise by specifying exactly what we mean by work13

Work =Energy more than just unpleasant tasks13

bull  In physics the definition of work is the application of a force through a distance Energy is needed to do it13

13 13W = Fd13

bull  W is the work done = energy used13bull  F is the force applied13bull  d is the distance through which the force acts13bull  Only the force that acts in the direction of motion counts

towards work13

1113

Okay what is Force then13bull  Force is a pushingpulling agent13bull  Examples13

ndash  gravity exerts a downward force on you13ndash  the floor exerts an upward force on a ball during its bounce13ndash  a car seat exerts a forward force on your body when you accelerate forward from

a stop13ndash  the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)13ndash  you exert a sideways force on a couch that you slide across the floor13ndash  a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your head13ndash  the expanding gas in your carrsquos cylinder exerts a force against the piston13

Forces have Direction13bull  In all the previous examples force had a

direction associated with it13bull  If multiple forces act on an object they

could potentially add or cancel depending on direction13

Force 1 Force 2

Total Force Force 1

Force 2

Total Force = 0

1213

When net force is not zero13bull  When an object experiences a non-zero net force it must

accelerate13bull  Newtonrsquos second law1313 13F = ma 13Force = mass times acceleration13

bull  The same force makes a small object accelerate more than it would a more massive object13ndash  hit a golf ball and a bowling ball with a golf club and see what

happens13

Question13A 150 lb person is standing still on the edge of a cliff What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

1313

Question13A 150 lb person jumps (or was he pushed) off a cliff and is falling to their death What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

But what is acceleration13

bull  This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellip13

bull  Acceleration is any change in velocity (speed andor direction of motion)13

bull  Measured as rate of change of velocity13ndash  velocity is expressed in meters per second (ms)13ndash  acceleration is meters per second per second13ndash  expressed as ms2 (meters per second-squared)13

1413

Putting it back together Units of Energy13

bull  Force is a mass times an acceleration (F=ma)13ndash  mass has units of kilograms13ndash  acceleration is ms213ndash  force is then kgms2 which we call Newtons (N)13

bull  Work is a force times a distance (W=Fd)13ndash  units are then (kgms2)m = kg m2s2 = Nm = Joules (J)13ndash  One joule is one Newton of force acting through one meter13ndash  Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J13bull  Energy has the same units as work Joules13

A Zoo of Units13bull  The main metric unit of energy is the Joule and most of

the world uses this but many others exist13bull  The calorie is 4184 Joules13

ndash  raise 1 gram (cc) of water one degree Celsius13bull  The Calorie (kilocalorie) is 4184 J (used for food energy) 13

ndash  raise 1 kg (1 liter) of water one degree Celsius13bull  The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one match13ndash  raise 1 pound of water one degree Fahrenheit13

bull  The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860 Calories (used for electrical energy)13ndash  one Watt (W) is one Joule per second 13ndash  a kWh is 1000 W for one hour (3600 seconds)13

bull  Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feet of natural gas gram of Uranium or amount of any energy containing source etc13

1513

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

The Physics of Energy Formula List13bull  Lots of forms of energy coming fast and furious but to put

it in perspective herersquos a list of formulas13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

1613

Kinetic Energy13bull  Kinetic Energy the energy of motion13bull  Moving things carry energy in the amount1313 13 13KE = frac12mv213

bull  Note the v2 dependencemdashthis is why13ndash  a car at 60 mph is 4 times more dangerous than a car at 30 mph13ndash  hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force winds13ndash  a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you could shoot it13

Numerical examples of kinetic energy13

bull  A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy1313 13 13KE = frac12times(0145 kg)times(30 ms)21313 13 13 13= 6525 kgm2s2 asymp 65 J = 0016 Calories13

bull  A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy is1313 13 13 KE = frac12times(000567 kg)times(5 ms)21313 13 13 13= 007 kgm2s2 = 007 J13

1713

More numerical examples13

bull  A 1500 kg car moves down the freeway at 30 ms (67 mph)1313 13 KE = frac12times(1500 kg)times(30 ms)21313 13 13 13= 675000 kgm2s2 = 675 kJ13

Convert to Calories 4184 kJ = 1 Calorie13675 kJ (1 Calorie4184 kJ) = 161 Calorie13

bull  A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)1313 13 KE = frac12times(2 kg)times(1 ms)21313 13 13 13= 1 kgm2s2 = 1 J13

Question13Kinetic energy is E = 12 m v2 Which has more energy13

A 10 kg object going 100 ms13

B 100 kg object going 10 ms13

C 1 kg object going 1000 ms13

D 1000 kg object going 1 ms13

1 ms = 22 mph13

1813

Gravitational Potential Energy13bull  It takes work to lift a mass against the pull (force) of

gravity13bull  The force of gravity is mg where m is the mass and g is

the gravitational acceleration1313 13 13F = mg 13(note similarity to F = ma)13

ndash  g = 98 ms2 on the surface of the earth or 32 fts213bull  Lifting a height h against the gravitational force

requires an energy input (work) of1313 13ΔE = W = F h = mgh13

bull  Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below13

bull  Water in river or hydroelectric plant is using potential energy that it got from being lifted up when Sun (solar energy) evaporated the water13

Question13Potential energy is E = 10 m h (metric units) Which has more energy13

A 1 ton of water at a height of 100 ft 13

B 100 tons of water at a height of 1 ft 13

C 200 lb (110 ton) of water at 1000 ft13

D All of the above have same energy13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

913

We live in a special time and placehellip13bull  We use almost 100 times the amount used by the rest of the

world (by population)13bull  This phase has only lasted for the last century or so13bull  Most of our resources come from fossil fuels presently and

this has a short finite lifetime13bull  Fossil fuels formed from solar energy over 300 million

years will be used up in a few centuries13

2000 2500 3000 3500 4000 1500 1000 500 0

year

ener

gy u

sage

1013

Energy the capacity to do work13

bull  This notion makes sense even in a colloquial context13ndash  hard to get work done when yoursquore wiped out

(low on energy)13ndash work makes you tired yoursquove used up energy13

bull  But we can make this definition of energy much more precise by specifying exactly what we mean by work13

Work =Energy more than just unpleasant tasks13

bull  In physics the definition of work is the application of a force through a distance Energy is needed to do it13

13 13W = Fd13

bull  W is the work done = energy used13bull  F is the force applied13bull  d is the distance through which the force acts13bull  Only the force that acts in the direction of motion counts

towards work13

1113

Okay what is Force then13bull  Force is a pushingpulling agent13bull  Examples13

ndash  gravity exerts a downward force on you13ndash  the floor exerts an upward force on a ball during its bounce13ndash  a car seat exerts a forward force on your body when you accelerate forward from

a stop13ndash  the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)13ndash  you exert a sideways force on a couch that you slide across the floor13ndash  a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your head13ndash  the expanding gas in your carrsquos cylinder exerts a force against the piston13

Forces have Direction13bull  In all the previous examples force had a

direction associated with it13bull  If multiple forces act on an object they

could potentially add or cancel depending on direction13

Force 1 Force 2

Total Force Force 1

Force 2

Total Force = 0

1213

When net force is not zero13bull  When an object experiences a non-zero net force it must

accelerate13bull  Newtonrsquos second law1313 13F = ma 13Force = mass times acceleration13

bull  The same force makes a small object accelerate more than it would a more massive object13ndash  hit a golf ball and a bowling ball with a golf club and see what

happens13

Question13A 150 lb person is standing still on the edge of a cliff What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

1313

Question13A 150 lb person jumps (or was he pushed) off a cliff and is falling to their death What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

But what is acceleration13

bull  This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellip13

bull  Acceleration is any change in velocity (speed andor direction of motion)13

bull  Measured as rate of change of velocity13ndash  velocity is expressed in meters per second (ms)13ndash  acceleration is meters per second per second13ndash  expressed as ms2 (meters per second-squared)13

1413

Putting it back together Units of Energy13

bull  Force is a mass times an acceleration (F=ma)13ndash  mass has units of kilograms13ndash  acceleration is ms213ndash  force is then kgms2 which we call Newtons (N)13

bull  Work is a force times a distance (W=Fd)13ndash  units are then (kgms2)m = kg m2s2 = Nm = Joules (J)13ndash  One joule is one Newton of force acting through one meter13ndash  Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J13bull  Energy has the same units as work Joules13

A Zoo of Units13bull  The main metric unit of energy is the Joule and most of

the world uses this but many others exist13bull  The calorie is 4184 Joules13

ndash  raise 1 gram (cc) of water one degree Celsius13bull  The Calorie (kilocalorie) is 4184 J (used for food energy) 13

ndash  raise 1 kg (1 liter) of water one degree Celsius13bull  The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one match13ndash  raise 1 pound of water one degree Fahrenheit13

bull  The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860 Calories (used for electrical energy)13ndash  one Watt (W) is one Joule per second 13ndash  a kWh is 1000 W for one hour (3600 seconds)13

bull  Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feet of natural gas gram of Uranium or amount of any energy containing source etc13

1513

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

The Physics of Energy Formula List13bull  Lots of forms of energy coming fast and furious but to put

it in perspective herersquos a list of formulas13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

1613

Kinetic Energy13bull  Kinetic Energy the energy of motion13bull  Moving things carry energy in the amount1313 13 13KE = frac12mv213

bull  Note the v2 dependencemdashthis is why13ndash  a car at 60 mph is 4 times more dangerous than a car at 30 mph13ndash  hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force winds13ndash  a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you could shoot it13

Numerical examples of kinetic energy13

bull  A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy1313 13 13KE = frac12times(0145 kg)times(30 ms)21313 13 13 13= 6525 kgm2s2 asymp 65 J = 0016 Calories13

bull  A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy is1313 13 13 KE = frac12times(000567 kg)times(5 ms)21313 13 13 13= 007 kgm2s2 = 007 J13

1713

More numerical examples13

bull  A 1500 kg car moves down the freeway at 30 ms (67 mph)1313 13 KE = frac12times(1500 kg)times(30 ms)21313 13 13 13= 675000 kgm2s2 = 675 kJ13

Convert to Calories 4184 kJ = 1 Calorie13675 kJ (1 Calorie4184 kJ) = 161 Calorie13

bull  A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)1313 13 KE = frac12times(2 kg)times(1 ms)21313 13 13 13= 1 kgm2s2 = 1 J13

Question13Kinetic energy is E = 12 m v2 Which has more energy13

A 10 kg object going 100 ms13

B 100 kg object going 10 ms13

C 1 kg object going 1000 ms13

D 1000 kg object going 1 ms13

1 ms = 22 mph13

1813

Gravitational Potential Energy13bull  It takes work to lift a mass against the pull (force) of

gravity13bull  The force of gravity is mg where m is the mass and g is

the gravitational acceleration1313 13 13F = mg 13(note similarity to F = ma)13

ndash  g = 98 ms2 on the surface of the earth or 32 fts213bull  Lifting a height h against the gravitational force

requires an energy input (work) of1313 13ΔE = W = F h = mgh13

bull  Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below13

bull  Water in river or hydroelectric plant is using potential energy that it got from being lifted up when Sun (solar energy) evaporated the water13

Question13Potential energy is E = 10 m h (metric units) Which has more energy13

A 1 ton of water at a height of 100 ft 13

B 100 tons of water at a height of 1 ft 13

C 200 lb (110 ton) of water at 1000 ft13

D All of the above have same energy13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

1013

Energy the capacity to do work13

bull  This notion makes sense even in a colloquial context13ndash  hard to get work done when yoursquore wiped out

(low on energy)13ndash work makes you tired yoursquove used up energy13

bull  But we can make this definition of energy much more precise by specifying exactly what we mean by work13

Work =Energy more than just unpleasant tasks13

bull  In physics the definition of work is the application of a force through a distance Energy is needed to do it13

13 13W = Fd13

bull  W is the work done = energy used13bull  F is the force applied13bull  d is the distance through which the force acts13bull  Only the force that acts in the direction of motion counts

towards work13

1113

Okay what is Force then13bull  Force is a pushingpulling agent13bull  Examples13

ndash  gravity exerts a downward force on you13ndash  the floor exerts an upward force on a ball during its bounce13ndash  a car seat exerts a forward force on your body when you accelerate forward from

a stop13ndash  the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)13ndash  you exert a sideways force on a couch that you slide across the floor13ndash  a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your head13ndash  the expanding gas in your carrsquos cylinder exerts a force against the piston13

Forces have Direction13bull  In all the previous examples force had a

direction associated with it13bull  If multiple forces act on an object they

could potentially add or cancel depending on direction13

Force 1 Force 2

Total Force Force 1

Force 2

Total Force = 0

1213

When net force is not zero13bull  When an object experiences a non-zero net force it must

accelerate13bull  Newtonrsquos second law1313 13F = ma 13Force = mass times acceleration13

bull  The same force makes a small object accelerate more than it would a more massive object13ndash  hit a golf ball and a bowling ball with a golf club and see what

happens13

Question13A 150 lb person is standing still on the edge of a cliff What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

1313

Question13A 150 lb person jumps (or was he pushed) off a cliff and is falling to their death What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

But what is acceleration13

bull  This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellip13

bull  Acceleration is any change in velocity (speed andor direction of motion)13

bull  Measured as rate of change of velocity13ndash  velocity is expressed in meters per second (ms)13ndash  acceleration is meters per second per second13ndash  expressed as ms2 (meters per second-squared)13

1413

Putting it back together Units of Energy13

bull  Force is a mass times an acceleration (F=ma)13ndash  mass has units of kilograms13ndash  acceleration is ms213ndash  force is then kgms2 which we call Newtons (N)13

bull  Work is a force times a distance (W=Fd)13ndash  units are then (kgms2)m = kg m2s2 = Nm = Joules (J)13ndash  One joule is one Newton of force acting through one meter13ndash  Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J13bull  Energy has the same units as work Joules13

A Zoo of Units13bull  The main metric unit of energy is the Joule and most of

the world uses this but many others exist13bull  The calorie is 4184 Joules13

ndash  raise 1 gram (cc) of water one degree Celsius13bull  The Calorie (kilocalorie) is 4184 J (used for food energy) 13

ndash  raise 1 kg (1 liter) of water one degree Celsius13bull  The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one match13ndash  raise 1 pound of water one degree Fahrenheit13

bull  The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860 Calories (used for electrical energy)13ndash  one Watt (W) is one Joule per second 13ndash  a kWh is 1000 W for one hour (3600 seconds)13

bull  Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feet of natural gas gram of Uranium or amount of any energy containing source etc13

1513

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

The Physics of Energy Formula List13bull  Lots of forms of energy coming fast and furious but to put

it in perspective herersquos a list of formulas13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

1613

Kinetic Energy13bull  Kinetic Energy the energy of motion13bull  Moving things carry energy in the amount1313 13 13KE = frac12mv213

bull  Note the v2 dependencemdashthis is why13ndash  a car at 60 mph is 4 times more dangerous than a car at 30 mph13ndash  hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force winds13ndash  a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you could shoot it13

Numerical examples of kinetic energy13

bull  A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy1313 13 13KE = frac12times(0145 kg)times(30 ms)21313 13 13 13= 6525 kgm2s2 asymp 65 J = 0016 Calories13

bull  A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy is1313 13 13 KE = frac12times(000567 kg)times(5 ms)21313 13 13 13= 007 kgm2s2 = 007 J13

1713

More numerical examples13

bull  A 1500 kg car moves down the freeway at 30 ms (67 mph)1313 13 KE = frac12times(1500 kg)times(30 ms)21313 13 13 13= 675000 kgm2s2 = 675 kJ13

Convert to Calories 4184 kJ = 1 Calorie13675 kJ (1 Calorie4184 kJ) = 161 Calorie13

bull  A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)1313 13 KE = frac12times(2 kg)times(1 ms)21313 13 13 13= 1 kgm2s2 = 1 J13

Question13Kinetic energy is E = 12 m v2 Which has more energy13

A 10 kg object going 100 ms13

B 100 kg object going 10 ms13

C 1 kg object going 1000 ms13

D 1000 kg object going 1 ms13

1 ms = 22 mph13

1813

Gravitational Potential Energy13bull  It takes work to lift a mass against the pull (force) of

gravity13bull  The force of gravity is mg where m is the mass and g is

the gravitational acceleration1313 13 13F = mg 13(note similarity to F = ma)13

ndash  g = 98 ms2 on the surface of the earth or 32 fts213bull  Lifting a height h against the gravitational force

requires an energy input (work) of1313 13ΔE = W = F h = mgh13

bull  Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below13

bull  Water in river or hydroelectric plant is using potential energy that it got from being lifted up when Sun (solar energy) evaporated the water13

Question13Potential energy is E = 10 m h (metric units) Which has more energy13

A 1 ton of water at a height of 100 ft 13

B 100 tons of water at a height of 1 ft 13

C 200 lb (110 ton) of water at 1000 ft13

D All of the above have same energy13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

1113

Okay what is Force then13bull  Force is a pushingpulling agent13bull  Examples13

ndash  gravity exerts a downward force on you13ndash  the floor exerts an upward force on a ball during its bounce13ndash  a car seat exerts a forward force on your body when you accelerate forward from

a stop13ndash  the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)13ndash  you exert a sideways force on a couch that you slide across the floor13ndash  a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your head13ndash  the expanding gas in your carrsquos cylinder exerts a force against the piston13

Forces have Direction13bull  In all the previous examples force had a

direction associated with it13bull  If multiple forces act on an object they

could potentially add or cancel depending on direction13

Force 1 Force 2

Total Force Force 1

Force 2

Total Force = 0

1213

When net force is not zero13bull  When an object experiences a non-zero net force it must

accelerate13bull  Newtonrsquos second law1313 13F = ma 13Force = mass times acceleration13

bull  The same force makes a small object accelerate more than it would a more massive object13ndash  hit a golf ball and a bowling ball with a golf club and see what

happens13

Question13A 150 lb person is standing still on the edge of a cliff What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

1313

Question13A 150 lb person jumps (or was he pushed) off a cliff and is falling to their death What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

But what is acceleration13

bull  This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellip13

bull  Acceleration is any change in velocity (speed andor direction of motion)13

bull  Measured as rate of change of velocity13ndash  velocity is expressed in meters per second (ms)13ndash  acceleration is meters per second per second13ndash  expressed as ms2 (meters per second-squared)13

1413

Putting it back together Units of Energy13

bull  Force is a mass times an acceleration (F=ma)13ndash  mass has units of kilograms13ndash  acceleration is ms213ndash  force is then kgms2 which we call Newtons (N)13

bull  Work is a force times a distance (W=Fd)13ndash  units are then (kgms2)m = kg m2s2 = Nm = Joules (J)13ndash  One joule is one Newton of force acting through one meter13ndash  Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J13bull  Energy has the same units as work Joules13

A Zoo of Units13bull  The main metric unit of energy is the Joule and most of

the world uses this but many others exist13bull  The calorie is 4184 Joules13

ndash  raise 1 gram (cc) of water one degree Celsius13bull  The Calorie (kilocalorie) is 4184 J (used for food energy) 13

ndash  raise 1 kg (1 liter) of water one degree Celsius13bull  The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one match13ndash  raise 1 pound of water one degree Fahrenheit13

bull  The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860 Calories (used for electrical energy)13ndash  one Watt (W) is one Joule per second 13ndash  a kWh is 1000 W for one hour (3600 seconds)13

bull  Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feet of natural gas gram of Uranium or amount of any energy containing source etc13

1513

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

The Physics of Energy Formula List13bull  Lots of forms of energy coming fast and furious but to put

it in perspective herersquos a list of formulas13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

1613

Kinetic Energy13bull  Kinetic Energy the energy of motion13bull  Moving things carry energy in the amount1313 13 13KE = frac12mv213

bull  Note the v2 dependencemdashthis is why13ndash  a car at 60 mph is 4 times more dangerous than a car at 30 mph13ndash  hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force winds13ndash  a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you could shoot it13

Numerical examples of kinetic energy13

bull  A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy1313 13 13KE = frac12times(0145 kg)times(30 ms)21313 13 13 13= 6525 kgm2s2 asymp 65 J = 0016 Calories13

bull  A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy is1313 13 13 KE = frac12times(000567 kg)times(5 ms)21313 13 13 13= 007 kgm2s2 = 007 J13

1713

More numerical examples13

bull  A 1500 kg car moves down the freeway at 30 ms (67 mph)1313 13 KE = frac12times(1500 kg)times(30 ms)21313 13 13 13= 675000 kgm2s2 = 675 kJ13

Convert to Calories 4184 kJ = 1 Calorie13675 kJ (1 Calorie4184 kJ) = 161 Calorie13

bull  A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)1313 13 KE = frac12times(2 kg)times(1 ms)21313 13 13 13= 1 kgm2s2 = 1 J13

Question13Kinetic energy is E = 12 m v2 Which has more energy13

A 10 kg object going 100 ms13

B 100 kg object going 10 ms13

C 1 kg object going 1000 ms13

D 1000 kg object going 1 ms13

1 ms = 22 mph13

1813

Gravitational Potential Energy13bull  It takes work to lift a mass against the pull (force) of

gravity13bull  The force of gravity is mg where m is the mass and g is

the gravitational acceleration1313 13 13F = mg 13(note similarity to F = ma)13

ndash  g = 98 ms2 on the surface of the earth or 32 fts213bull  Lifting a height h against the gravitational force

requires an energy input (work) of1313 13ΔE = W = F h = mgh13

bull  Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below13

bull  Water in river or hydroelectric plant is using potential energy that it got from being lifted up when Sun (solar energy) evaporated the water13

Question13Potential energy is E = 10 m h (metric units) Which has more energy13

A 1 ton of water at a height of 100 ft 13

B 100 tons of water at a height of 1 ft 13

C 200 lb (110 ton) of water at 1000 ft13

D All of the above have same energy13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

1213

When net force is not zero13bull  When an object experiences a non-zero net force it must

accelerate13bull  Newtonrsquos second law1313 13F = ma 13Force = mass times acceleration13

bull  The same force makes a small object accelerate more than it would a more massive object13ndash  hit a golf ball and a bowling ball with a golf club and see what

happens13

Question13A 150 lb person is standing still on the edge of a cliff What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

1313

Question13A 150 lb person jumps (or was he pushed) off a cliff and is falling to their death What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

But what is acceleration13

bull  This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellip13

bull  Acceleration is any change in velocity (speed andor direction of motion)13

bull  Measured as rate of change of velocity13ndash  velocity is expressed in meters per second (ms)13ndash  acceleration is meters per second per second13ndash  expressed as ms2 (meters per second-squared)13

1413

Putting it back together Units of Energy13

bull  Force is a mass times an acceleration (F=ma)13ndash  mass has units of kilograms13ndash  acceleration is ms213ndash  force is then kgms2 which we call Newtons (N)13

bull  Work is a force times a distance (W=Fd)13ndash  units are then (kgms2)m = kg m2s2 = Nm = Joules (J)13ndash  One joule is one Newton of force acting through one meter13ndash  Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J13bull  Energy has the same units as work Joules13

A Zoo of Units13bull  The main metric unit of energy is the Joule and most of

the world uses this but many others exist13bull  The calorie is 4184 Joules13

ndash  raise 1 gram (cc) of water one degree Celsius13bull  The Calorie (kilocalorie) is 4184 J (used for food energy) 13

ndash  raise 1 kg (1 liter) of water one degree Celsius13bull  The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one match13ndash  raise 1 pound of water one degree Fahrenheit13

bull  The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860 Calories (used for electrical energy)13ndash  one Watt (W) is one Joule per second 13ndash  a kWh is 1000 W for one hour (3600 seconds)13

bull  Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feet of natural gas gram of Uranium or amount of any energy containing source etc13

1513

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

The Physics of Energy Formula List13bull  Lots of forms of energy coming fast and furious but to put

it in perspective herersquos a list of formulas13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

1613

Kinetic Energy13bull  Kinetic Energy the energy of motion13bull  Moving things carry energy in the amount1313 13 13KE = frac12mv213

bull  Note the v2 dependencemdashthis is why13ndash  a car at 60 mph is 4 times more dangerous than a car at 30 mph13ndash  hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force winds13ndash  a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you could shoot it13

Numerical examples of kinetic energy13

bull  A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy1313 13 13KE = frac12times(0145 kg)times(30 ms)21313 13 13 13= 6525 kgm2s2 asymp 65 J = 0016 Calories13

bull  A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy is1313 13 13 KE = frac12times(000567 kg)times(5 ms)21313 13 13 13= 007 kgm2s2 = 007 J13

1713

More numerical examples13

bull  A 1500 kg car moves down the freeway at 30 ms (67 mph)1313 13 KE = frac12times(1500 kg)times(30 ms)21313 13 13 13= 675000 kgm2s2 = 675 kJ13

Convert to Calories 4184 kJ = 1 Calorie13675 kJ (1 Calorie4184 kJ) = 161 Calorie13

bull  A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)1313 13 KE = frac12times(2 kg)times(1 ms)21313 13 13 13= 1 kgm2s2 = 1 J13

Question13Kinetic energy is E = 12 m v2 Which has more energy13

A 10 kg object going 100 ms13

B 100 kg object going 10 ms13

C 1 kg object going 1000 ms13

D 1000 kg object going 1 ms13

1 ms = 22 mph13

1813

Gravitational Potential Energy13bull  It takes work to lift a mass against the pull (force) of

gravity13bull  The force of gravity is mg where m is the mass and g is

the gravitational acceleration1313 13 13F = mg 13(note similarity to F = ma)13

ndash  g = 98 ms2 on the surface of the earth or 32 fts213bull  Lifting a height h against the gravitational force

requires an energy input (work) of1313 13ΔE = W = F h = mgh13

bull  Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below13

bull  Water in river or hydroelectric plant is using potential energy that it got from being lifted up when Sun (solar energy) evaporated the water13

Question13Potential energy is E = 10 m h (metric units) Which has more energy13

A 1 ton of water at a height of 100 ft 13

B 100 tons of water at a height of 1 ft 13

C 200 lb (110 ton) of water at 1000 ft13

D All of the above have same energy13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

1313

Question13A 150 lb person jumps (or was he pushed) off a cliff and is falling to their death What is the total force on the person 13

A zero13B 150 lb13C Canrsquot say from this info13

But what is acceleration13

bull  This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellip13

bull  Acceleration is any change in velocity (speed andor direction of motion)13

bull  Measured as rate of change of velocity13ndash  velocity is expressed in meters per second (ms)13ndash  acceleration is meters per second per second13ndash  expressed as ms2 (meters per second-squared)13

1413

Putting it back together Units of Energy13

bull  Force is a mass times an acceleration (F=ma)13ndash  mass has units of kilograms13ndash  acceleration is ms213ndash  force is then kgms2 which we call Newtons (N)13

bull  Work is a force times a distance (W=Fd)13ndash  units are then (kgms2)m = kg m2s2 = Nm = Joules (J)13ndash  One joule is one Newton of force acting through one meter13ndash  Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J13bull  Energy has the same units as work Joules13

A Zoo of Units13bull  The main metric unit of energy is the Joule and most of

the world uses this but many others exist13bull  The calorie is 4184 Joules13

ndash  raise 1 gram (cc) of water one degree Celsius13bull  The Calorie (kilocalorie) is 4184 J (used for food energy) 13

ndash  raise 1 kg (1 liter) of water one degree Celsius13bull  The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one match13ndash  raise 1 pound of water one degree Fahrenheit13

bull  The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860 Calories (used for electrical energy)13ndash  one Watt (W) is one Joule per second 13ndash  a kWh is 1000 W for one hour (3600 seconds)13

bull  Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feet of natural gas gram of Uranium or amount of any energy containing source etc13

1513

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

The Physics of Energy Formula List13bull  Lots of forms of energy coming fast and furious but to put

it in perspective herersquos a list of formulas13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

1613

Kinetic Energy13bull  Kinetic Energy the energy of motion13bull  Moving things carry energy in the amount1313 13 13KE = frac12mv213

bull  Note the v2 dependencemdashthis is why13ndash  a car at 60 mph is 4 times more dangerous than a car at 30 mph13ndash  hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force winds13ndash  a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you could shoot it13

Numerical examples of kinetic energy13

bull  A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy1313 13 13KE = frac12times(0145 kg)times(30 ms)21313 13 13 13= 6525 kgm2s2 asymp 65 J = 0016 Calories13

bull  A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy is1313 13 13 KE = frac12times(000567 kg)times(5 ms)21313 13 13 13= 007 kgm2s2 = 007 J13

1713

More numerical examples13

bull  A 1500 kg car moves down the freeway at 30 ms (67 mph)1313 13 KE = frac12times(1500 kg)times(30 ms)21313 13 13 13= 675000 kgm2s2 = 675 kJ13

Convert to Calories 4184 kJ = 1 Calorie13675 kJ (1 Calorie4184 kJ) = 161 Calorie13

bull  A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)1313 13 KE = frac12times(2 kg)times(1 ms)21313 13 13 13= 1 kgm2s2 = 1 J13

Question13Kinetic energy is E = 12 m v2 Which has more energy13

A 10 kg object going 100 ms13

B 100 kg object going 10 ms13

C 1 kg object going 1000 ms13

D 1000 kg object going 1 ms13

1 ms = 22 mph13

1813

Gravitational Potential Energy13bull  It takes work to lift a mass against the pull (force) of

gravity13bull  The force of gravity is mg where m is the mass and g is

the gravitational acceleration1313 13 13F = mg 13(note similarity to F = ma)13

ndash  g = 98 ms2 on the surface of the earth or 32 fts213bull  Lifting a height h against the gravitational force

requires an energy input (work) of1313 13ΔE = W = F h = mgh13

bull  Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below13

bull  Water in river or hydroelectric plant is using potential energy that it got from being lifted up when Sun (solar energy) evaporated the water13

Question13Potential energy is E = 10 m h (metric units) Which has more energy13

A 1 ton of water at a height of 100 ft 13

B 100 tons of water at a height of 1 ft 13

C 200 lb (110 ton) of water at 1000 ft13

D All of the above have same energy13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

1413

Putting it back together Units of Energy13

bull  Force is a mass times an acceleration (F=ma)13ndash  mass has units of kilograms13ndash  acceleration is ms213ndash  force is then kgms2 which we call Newtons (N)13

bull  Work is a force times a distance (W=Fd)13ndash  units are then (kgms2)m = kg m2s2 = Nm = Joules (J)13ndash  One joule is one Newton of force acting through one meter13ndash  Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J13bull  Energy has the same units as work Joules13

A Zoo of Units13bull  The main metric unit of energy is the Joule and most of

the world uses this but many others exist13bull  The calorie is 4184 Joules13

ndash  raise 1 gram (cc) of water one degree Celsius13bull  The Calorie (kilocalorie) is 4184 J (used for food energy) 13

ndash  raise 1 kg (1 liter) of water one degree Celsius13bull  The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one match13ndash  raise 1 pound of water one degree Fahrenheit13

bull  The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860 Calories (used for electrical energy)13ndash  one Watt (W) is one Joule per second 13ndash  a kWh is 1000 W for one hour (3600 seconds)13

bull  Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feet of natural gas gram of Uranium or amount of any energy containing source etc13

1513

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

The Physics of Energy Formula List13bull  Lots of forms of energy coming fast and furious but to put

it in perspective herersquos a list of formulas13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

1613

Kinetic Energy13bull  Kinetic Energy the energy of motion13bull  Moving things carry energy in the amount1313 13 13KE = frac12mv213

bull  Note the v2 dependencemdashthis is why13ndash  a car at 60 mph is 4 times more dangerous than a car at 30 mph13ndash  hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force winds13ndash  a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you could shoot it13

Numerical examples of kinetic energy13

bull  A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy1313 13 13KE = frac12times(0145 kg)times(30 ms)21313 13 13 13= 6525 kgm2s2 asymp 65 J = 0016 Calories13

bull  A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy is1313 13 13 KE = frac12times(000567 kg)times(5 ms)21313 13 13 13= 007 kgm2s2 = 007 J13

1713

More numerical examples13

bull  A 1500 kg car moves down the freeway at 30 ms (67 mph)1313 13 KE = frac12times(1500 kg)times(30 ms)21313 13 13 13= 675000 kgm2s2 = 675 kJ13

Convert to Calories 4184 kJ = 1 Calorie13675 kJ (1 Calorie4184 kJ) = 161 Calorie13

bull  A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)1313 13 KE = frac12times(2 kg)times(1 ms)21313 13 13 13= 1 kgm2s2 = 1 J13

Question13Kinetic energy is E = 12 m v2 Which has more energy13

A 10 kg object going 100 ms13

B 100 kg object going 10 ms13

C 1 kg object going 1000 ms13

D 1000 kg object going 1 ms13

1 ms = 22 mph13

1813

Gravitational Potential Energy13bull  It takes work to lift a mass against the pull (force) of

gravity13bull  The force of gravity is mg where m is the mass and g is

the gravitational acceleration1313 13 13F = mg 13(note similarity to F = ma)13

ndash  g = 98 ms2 on the surface of the earth or 32 fts213bull  Lifting a height h against the gravitational force

requires an energy input (work) of1313 13ΔE = W = F h = mgh13

bull  Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below13

bull  Water in river or hydroelectric plant is using potential energy that it got from being lifted up when Sun (solar energy) evaporated the water13

Question13Potential energy is E = 10 m h (metric units) Which has more energy13

A 1 ton of water at a height of 100 ft 13

B 100 tons of water at a height of 1 ft 13

C 200 lb (110 ton) of water at 1000 ft13

D All of the above have same energy13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

1513

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

The Physics of Energy Formula List13bull  Lots of forms of energy coming fast and furious but to put

it in perspective herersquos a list of formulas13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

1613

Kinetic Energy13bull  Kinetic Energy the energy of motion13bull  Moving things carry energy in the amount1313 13 13KE = frac12mv213

bull  Note the v2 dependencemdashthis is why13ndash  a car at 60 mph is 4 times more dangerous than a car at 30 mph13ndash  hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force winds13ndash  a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you could shoot it13

Numerical examples of kinetic energy13

bull  A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy1313 13 13KE = frac12times(0145 kg)times(30 ms)21313 13 13 13= 6525 kgm2s2 asymp 65 J = 0016 Calories13

bull  A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy is1313 13 13 KE = frac12times(000567 kg)times(5 ms)21313 13 13 13= 007 kgm2s2 = 007 J13

1713

More numerical examples13

bull  A 1500 kg car moves down the freeway at 30 ms (67 mph)1313 13 KE = frac12times(1500 kg)times(30 ms)21313 13 13 13= 675000 kgm2s2 = 675 kJ13

Convert to Calories 4184 kJ = 1 Calorie13675 kJ (1 Calorie4184 kJ) = 161 Calorie13

bull  A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)1313 13 KE = frac12times(2 kg)times(1 ms)21313 13 13 13= 1 kgm2s2 = 1 J13

Question13Kinetic energy is E = 12 m v2 Which has more energy13

A 10 kg object going 100 ms13

B 100 kg object going 10 ms13

C 1 kg object going 1000 ms13

D 1000 kg object going 1 ms13

1 ms = 22 mph13

1813

Gravitational Potential Energy13bull  It takes work to lift a mass against the pull (force) of

gravity13bull  The force of gravity is mg where m is the mass and g is

the gravitational acceleration1313 13 13F = mg 13(note similarity to F = ma)13

ndash  g = 98 ms2 on the surface of the earth or 32 fts213bull  Lifting a height h against the gravitational force

requires an energy input (work) of1313 13ΔE = W = F h = mgh13

bull  Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below13

bull  Water in river or hydroelectric plant is using potential energy that it got from being lifted up when Sun (solar energy) evaporated the water13

Question13Potential energy is E = 10 m h (metric units) Which has more energy13

A 1 ton of water at a height of 100 ft 13

B 100 tons of water at a height of 1 ft 13

C 200 lb (110 ton) of water at 1000 ft13

D All of the above have same energy13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

1613

Kinetic Energy13bull  Kinetic Energy the energy of motion13bull  Moving things carry energy in the amount1313 13 13KE = frac12mv213

bull  Note the v2 dependencemdashthis is why13ndash  a car at 60 mph is 4 times more dangerous than a car at 30 mph13ndash  hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force winds13ndash  a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you could shoot it13

Numerical examples of kinetic energy13

bull  A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy1313 13 13KE = frac12times(0145 kg)times(30 ms)21313 13 13 13= 6525 kgm2s2 asymp 65 J = 0016 Calories13

bull  A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy is1313 13 13 KE = frac12times(000567 kg)times(5 ms)21313 13 13 13= 007 kgm2s2 = 007 J13

1713

More numerical examples13

bull  A 1500 kg car moves down the freeway at 30 ms (67 mph)1313 13 KE = frac12times(1500 kg)times(30 ms)21313 13 13 13= 675000 kgm2s2 = 675 kJ13

Convert to Calories 4184 kJ = 1 Calorie13675 kJ (1 Calorie4184 kJ) = 161 Calorie13

bull  A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)1313 13 KE = frac12times(2 kg)times(1 ms)21313 13 13 13= 1 kgm2s2 = 1 J13

Question13Kinetic energy is E = 12 m v2 Which has more energy13

A 10 kg object going 100 ms13

B 100 kg object going 10 ms13

C 1 kg object going 1000 ms13

D 1000 kg object going 1 ms13

1 ms = 22 mph13

1813

Gravitational Potential Energy13bull  It takes work to lift a mass against the pull (force) of

gravity13bull  The force of gravity is mg where m is the mass and g is

the gravitational acceleration1313 13 13F = mg 13(note similarity to F = ma)13

ndash  g = 98 ms2 on the surface of the earth or 32 fts213bull  Lifting a height h against the gravitational force

requires an energy input (work) of1313 13ΔE = W = F h = mgh13

bull  Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below13

bull  Water in river or hydroelectric plant is using potential energy that it got from being lifted up when Sun (solar energy) evaporated the water13

Question13Potential energy is E = 10 m h (metric units) Which has more energy13

A 1 ton of water at a height of 100 ft 13

B 100 tons of water at a height of 1 ft 13

C 200 lb (110 ton) of water at 1000 ft13

D All of the above have same energy13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

1713

More numerical examples13

bull  A 1500 kg car moves down the freeway at 30 ms (67 mph)1313 13 KE = frac12times(1500 kg)times(30 ms)21313 13 13 13= 675000 kgm2s2 = 675 kJ13

Convert to Calories 4184 kJ = 1 Calorie13675 kJ (1 Calorie4184 kJ) = 161 Calorie13

bull  A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)1313 13 KE = frac12times(2 kg)times(1 ms)21313 13 13 13= 1 kgm2s2 = 1 J13

Question13Kinetic energy is E = 12 m v2 Which has more energy13

A 10 kg object going 100 ms13

B 100 kg object going 10 ms13

C 1 kg object going 1000 ms13

D 1000 kg object going 1 ms13

1 ms = 22 mph13

1813

Gravitational Potential Energy13bull  It takes work to lift a mass against the pull (force) of

gravity13bull  The force of gravity is mg where m is the mass and g is

the gravitational acceleration1313 13 13F = mg 13(note similarity to F = ma)13

ndash  g = 98 ms2 on the surface of the earth or 32 fts213bull  Lifting a height h against the gravitational force

requires an energy input (work) of1313 13ΔE = W = F h = mgh13

bull  Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below13

bull  Water in river or hydroelectric plant is using potential energy that it got from being lifted up when Sun (solar energy) evaporated the water13

Question13Potential energy is E = 10 m h (metric units) Which has more energy13

A 1 ton of water at a height of 100 ft 13

B 100 tons of water at a height of 1 ft 13

C 200 lb (110 ton) of water at 1000 ft13

D All of the above have same energy13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

1813

Gravitational Potential Energy13bull  It takes work to lift a mass against the pull (force) of

gravity13bull  The force of gravity is mg where m is the mass and g is

the gravitational acceleration1313 13 13F = mg 13(note similarity to F = ma)13

ndash  g = 98 ms2 on the surface of the earth or 32 fts213bull  Lifting a height h against the gravitational force

requires an energy input (work) of1313 13ΔE = W = F h = mgh13

bull  Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below13

bull  Water in river or hydroelectric plant is using potential energy that it got from being lifted up when Sun (solar energy) evaporated the water13

Question13Potential energy is E = 10 m h (metric units) Which has more energy13

A 1 ton of water at a height of 100 ft 13

B 100 tons of water at a height of 1 ft 13

C 200 lb (110 ton) of water at 1000 ft13

D All of the above have same energy13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

1913

First Example of Energy Exchange13bull  When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energy13bull  Where does this energy come from1313 13rArr from the gravitational potential energy13

bull  The higher the cliff the more kinetic energy the boulder will have when it reaches the ground13

mgh

becomes

frac12mv2

Energy is conserved so frac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

Examples of Gravitational Potential Energy13

bull  How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform1313 13 13mgh = (70 kg)times(10 ms2)times(10 m)1313 13 13 13= 7000 kgm2s2 = 7 kJ 13137 kJ (1 Calorie4182kJ) = 16 Calories 13

This is amount of energy the diver used in climbing the stairs (actually more than this since some energy was wasted) They got that energy from the food they ate13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

2013

The Energy of Heat13bull  Hot things have more energy than their cold

counterparts13bull  Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion of individual atomsmolecules13ndash  Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random13bull  Heat is frequently quantified by calories (or Btu)13

ndash  One calorie (4184 J) raises one gram of H2O 1ordmC13ndash  One Calorie (4184 J) raises one kilogram of H2O 1ordmC13ndash  One Btu (1055 J) raises one pound of H2O 1ordmF13

Energy of Heat continued13bull  Food Calories are with the ldquobigrdquo C or kilocalories (kcal)13bull  Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heats one liter of water 1ordmC In British Units 1 Btu heats 1 pound of water 1 degree Fahrenheit13ndash  these are useful numbers to hang onto13

bull  Example to heat a 2-liter bottle of Coke from the 5ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJ13

bull  Drink a pint (16 oz) of ice cold water (or coke) It weighs about 1 pound To heat it to body temperature (986 degrees minus 32 degrees or change of 666 degrees Takes about 67 Btu Convert to Calories 1 Calorie = 1kJ = 4 Btu so 13

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz of coke has 210 Calories and about 17 Calories are used just heating to your body temp you get less calories drinking it cold (or drinking quart of cold water ldquoburnsrdquo 17 Calories)13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

2113

The Physics of Energy Formula List13Energy Form13 Energy Formula13

Work13 W = Fd (Force times distance)13

Kinetic Energy13 KE = frac12mv2 (mass times velocity squared)13

(Grav) Potential Energy13 E = mgh (mass times height times 10ms2)13

Heat Energy13 ΔE = cpmΔT (mass times change in temperature times heat capacity)13

Mass energy13 E = mc2 (mass times speed of light squared)13

Radiative energy flux13 F = σT4 (temperature to the fourth power times a constant)13

Power (rate of energy use)13 P = ΔEΔt 13

Heat Capacity13bull  Different materials have different capacities to

hold heat13ndash  Add the same energy to different materials and yoursquoll

get different temperature rises13ndash  Quantified as heat capacity13ndash  Water is exceptional with 4184 JkgordmC13ndash  Most materials are about 1000 JkgordmC (including

wood air metals)13bull  Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we need1313air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)13

Important in designing solar heated houses Also reason it is cooler near the coast than inland13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

2213

Power13bull  Power is simply energy exchanged

per unit time or how fast you get work done (Watts = Joulessec) 13

bull  One horsepower = 745 W13bull  Perform 100 J of work in 1 s and

call it 100 W13bull  Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3 seconds rarr 700 W output13

bull  Shuttle puts out a few GW (gigawatts or 109 W) of power13

bull  A big electrical power plant puts out around a GW That is 1 Billion Joules per second House takes a few kW (kilowatt)13

Question13Power is Energy used per second P= energytime Which highest power 13

A Using 100 Calories in 10 minutes13

B Using 1000 Calories in 100 minutes13

C Using 10 Calories in 1 minute13

D Using 1 Calorie in 6 seconds13

E All of the above are the same power usage13

1 Calorieminute = Watts13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

2313

Wind Energy13

bull  Wind can be used as a source of energy (windmills sailing ships etc)13

bull  Really just kinetic energy13bull  Example wind passing through a square meter at 8 meters

per second13ndash  Each second we have 8 cubic meters13ndash  Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each second13ndash  frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 J13ndash  333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)13bull  Stronger winds rarr more power (like v2)13

Chemical Energy13

bull  Electrostatic energy (associated with charged particles like electrons) is stored in the chemical bonds of substances eg carbohydrates hydrocarbons13

bull  Rearranging these bonds can release energy (some reactions require energy to be put in)13

bull  Typical numbers are 100ndash200 kJ per mole13ndash  a mole is 6022times1023 moleculesparticles13ndash  typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules per gram or a few Calories per gram (remember 1 Cal = 1 kcal = 4187 J)13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

2413

Chemical Energy Examples13

bull  Burning a wooden match releases about one Btu or 1055 Joules (a match is about 03 grams) so this is gt3000 Jg nearly 1 Calg (450 Callb)13

bull  Burning coal releases about 20 kJ per gram of chemical energy or roughly 5 Calg (2300 Callb)13

bull  Burning gasoline yields about 39 kJ per gram or just over 9 Calg (4000 Callb)13

bull  Very few substances over about 11 Calg13bull  (1 Calg = 453 Callb)13

Energy from Food13

bull  We get the energy to do the things we do out of food (stored solar energy in the form of chemical energy)13

bull  Energy sources recognized by our digestive systems13ndash  Carbohydrates 134 Calories per gram13ndash  Proteins 4 Calories per gram13ndash  Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat than carbs or protein)13

ndash  Roughly 3500 Caloriespound in your body fat Less in your protein (muscle skin etc)13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

2513

Our Human Energy Budget13

bull  A 2000 Calorie per day diet means 2000times4184 J = 8368000 J per day13

bull  837 MJ in (24 hrday) times(60 minhr)times(60 secmin) = 86400 sec corresponds to 97 Watts of power13

bull  Even a couch-potato at 1500 Calday burns 75 W13

bull  More active lifestyles require greater Caloric intake (more energy)13

Nutrition Labels13bull  Nutrition labels tell you about the

energy content of food13bull  Note they use Calories with capitol C13bull  Conversions 13Fat 9 Calg1313 13 13 13Carbs 4 Calg1313 13 13 13Protein 4 Calg13

bull  This product has 72 Cal from fat 48 Cal from carbohydrates and 32 Cal from protein13ndash  sum is 152 Calories compare to label13

bull  152 Cal = 636 kJ enough to climb about 1000 meters (64 kg person)13

bull  1kwh = 860 Cal or about 14 lb body fat13

bull  1 gal of gas has 31000 Calories13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

2613

Mass-energy13bull  Einsteinrsquos famous relation1313 13E = mc21313relates mass to energy13

bull  In effect they are the same thing13ndash  one can be transformed into the other13ndash  physicists speak generally of mass-energy13

bull  Seldom experienced in daily life directly13ndash  Happens at large scale in the center of the sun and in

nuclear bombs and reactors13ndash  Actually does happen at barely detectable level in all

energy transactions but the effect is tiny13

E = mc2 Examples13bull  The energy equivalent of one gram of material

(any composition) is (0001 kg)times(30times108 ms)2 = 90times1013 J = 90000000000000 J = 90 TJ13ndash  Man thatrsquos big13ndash  Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)13bull  If one gram of material undergoes a chemical

reaction losing about 9000 J of energy how much mass does it lose13139000 J = Δmc2 so Δm = 9000c2 = 9times1039times10161313 13 13= 10-13 kg 13(would we ever notice)13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

2713

Solar Energy is Nuclear Using E = mc213

bull  Thermonuclear fusion reactions in the sunrsquos center13ndash  Sun is 16 million degrees Celsius in its center13ndash  Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then helium13ndash  Reaction per atom 20 million times more energetic than chemical

reactions in general13

4 protons mass = 4029

4He nucleus mass = 40015

2 neutrinos photons (light)

E = mc2 in Sun13

bull  Helium nucleus is lighter than the four protons13bull  Mass difference is 4029 - 40015 = 00276 amu13

ndash  1 amu (atomic mass unit) is 16605times10-27 kg13ndash  difference of 458times10-29 kg13ndash  multiply by c2 to get 412times10-12 J13ndash  1 mole (6022times1023 particles) of protons rarr 25times1012 J13ndash  typical chemical reactions are 100-200 kJmole13ndash  nuclear fusion is ~20 million times more potent stuff13ndash  Nuclear fusion is energy source of hydrogen bomb13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

2813

Energy from Light13bull  The tremendous energy from the sun is released as light So light

carries energy13bull  Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiation13bull  Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequency13bull  Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellip13bull  All objects emit ldquolightrdquo13bull  The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter more radiation and color is ldquobluerrdquo13

Emitted Radiationrsquos Color and Intensity depend on Temperature13

Object

You Heat Lamp Candle Flame Bulb Filament Sunrsquos Surface Neutron Star Molecules in deep space

Temperature

~ 30 C ~ 500 C ~ 1700 C ~ 2700 C ~ 5500 C ~ millions C

lt -272C

Color

Infrared (invisible) Dull red Dim orange Yellow Brilliant white X-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted light The hotter it gets the more intense the radiation (more energy)

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

2913

ldquoBlackbodyrdquo or Planck Spectrum13

Same thing on logarithmic scale13

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm (note 0degC = 273degK 300degK = 27degC = 81degF)

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

3013

Okay but how much energy13bull  The power given off of a surface in the form of light is

proportional to the fourth power of temperature1313 13 13F = σT4 in Watts per square meter13

ndash  the constant σ is numerically 567times10-8 WordmK4m213

ndash  easy to remember constant 567813ndash  temperature must be in Kelvin13

bull  ordmK = ordmC + 27313bull  ordmC = (59)times(ordmF ndash32)13

bull  Example radiation from your body13(567 times10-8) times(310)4 = 523 Watts per square meter13(if naked in the cold of space donrsquot let this happen to you)13

Radiant Energy continued13bull  Example The sun is 5800ordmK on its surface so13

F = σT4 = (567times10-8)times(5800)4 = 64times107 Wm213Summing over entire surface area of sun gives 1339times1026 W13

bull  Compare to total capacity of energy production on earth 33times1012 W13ndash  Single power plant typically 05ndash10 GW (109 W)13

bull  In earthly situations radiated power out partially balanced by radiated power in from other sources13ndash  Not 523 Wm2 in 70ordmF room more like 100 Wm213

bull  goes like σTh4 ndash σTc

413

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

3113

Electrical Energy13bull  Opposite charges attract so electrons are attracted to

protons This holds atoms together 13bull  It takes energy to pull electrons off their atoms13bull  Electrons want to get back home to their protons They can

only travel through conductors like wires not through insulators like plastic paper or wood They will go through miles of wire to get home to their protons 13

bull  This is how electricity works The electronrsquos energy can be stolen as it goes home Can be used in many many ways13

bull  Note electricity is not a primary source of energy Energy (from burning coal nat gas from hydro wind nuke or solar) is used to pull of electrons and that energy can be moved through wires and got back at will13

And those are the major playershellip13

bull  Wersquove now seen most of the major energy players13ndash  work as force times distance13ndash  kinetic energy (wind ocean currents)13ndash  gravitational potential energy (hydroelectric tidal)13ndash  chemical energy (fossil fuels batteries food biomass)13ndash  heat energy (power plants space heating)13ndash  mass-energy (nuclear sources sunrsquos energy)13ndash  radiant energy (solar energy)13ndash  electrical energy (energy of electrons separated from

their atoms)13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

3213

Conservation and Exchange of Energy13

Nothing Comes for Free13

Energy is Conserved13bull  Conservation of Energy is different from Energy

Conservation the latter being about using energy wisely13

bull  Conservation of Energy means energy is neither created nor destroyed The amount of energy in the Universe is constant13

bull  Donrsquot we create energy at a power plant13ndash  Oh that this were truemdashno we simply transform energy

at our power plants13bull  Doesnrsquot the sun create energy13

ndash  Nopemdashit exchanges mass for energy13bull  Donrsquot batteries give us new energy13

ndash  Nope just convert stored chemical energy to electrical energy Someone had to put that energy in there13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

3313

height reference h

Energy Exchange13bull  Though the total energy of a system is constant

the form of the energy can change13bull  A simple example is that of a simple pendulum in

which a continual exchange goes on between kinetic and potential energy13

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

Perpetual Motion13bull  Why wonrsquot the pendulum swing forever13bull  Itrsquos hard to design a system free of energy paths13bull  The pendulum slows down by several mechanisms13

ndash  Friction at the contact point requires force to oppose force acts through distance rarr work is done13

ndash  Air resistance must push through air with a force (through a distance) rarr work is done13

ndash  Gets some air swirling puts kinetic energy into air (not really fair to separate these last two)13

bull  Perpetual motion means no loss of energy13ndash  solar system orbits come very close13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

3413

Some Energy Chains13bull  A coffee mug with some gravitational potential

energy is dropped13bull  potential energy turns into kinetic energy13bull  kinetic energy of the mug goes into13

ndash  ripping the mug apart (chemical breaking bonds)13ndash  sending the pieces flying (kinetic)13ndash  into sound13ndash  into heating the floor and pieces through friction as the

pieces slide to a stop13bull  In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored in the potential energy)13

Gasoline Example13bull  Put gas in your car containing 9 Calg (31000 Calgallon)13bull  Combust gas turning 9 Calg into kinetic energy of

explosion13bull  Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a whole13bull  That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water and surrounding air) and friction of transmission system (heat) and noise of engine (heating the air) etc13

bull  Much of energy goes into stirring the air (ends up as heat)13bull  Apply the brakes and convert kinetic energy into heat13bull  It all ends up as waste heat ultimately13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

3513

Bouncing Ball13bull  Superball has gravitational potential energy13bull  Drop the ball and this becomes kinetic energy13bull  Ball hits ground and compresses (force times

distance) storing energy in the spring13bull  Ball releases this mechanically stored energy

and it goes back into kinetic form (bounces up)13

bull  Inefficiencies in ldquospringrdquo end up heating the ball and the floor and stirring the air a bit13

bull  In the end all is heat13

Why donrsquot we get hotter and hotter13

bull  If all these processes end up as heat why arenrsquot we continually getting hotter13

bull  If earth retained all its heat we would get hotter13bull  All of earthrsquos heat is radiated away1313 13F = σT413

bull  If we dump more power the temperature goes up the radiated power increases dramatically13ndash  comes to equilibrium power dumped = power radiated13ndash  stable against perturbation T tracks power budget13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

3613

Rough numbers13bull  How much power does the earth radiate13bull  F = σT4 for T = 288ordmK = 15ordmC is 390 Wm213bull  Summed over entire surface area (4πR2 where R

= 6378000 meters) is 20times1017 W13bull  Human global production is about 13times1012 W

(100 QBtuyr = 33TW World ~4 times more)13bull  Solar radiation incident on earth is 18times1017 W13

ndash  just solar luminosity of 39times1026 W divided by geometrical fraction that points at earth13

bull  Amazing coincidence of numbers (or is ithellip)13

No Energy for Free13

bull  No matter what you canrsquot create energy out of nothing it has to come from somewhere13

bull  We can transform energy from one form to another we can store energy we can utilize energy being conveyed from natural sources13

bull  The net energy of the entire Universe is constant13bull  The best we can do is scrape up some useful

crumbs13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

3713

Examples13bull  Unit conversion13

ndash  100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Cal13ndash  100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 J13ndash  100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWh13ndash  10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWh13ndash  How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86 Calorieshour About what average person eats13

ndash  Gasoline is $3gal Electricity if $015kWh Which is more expensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh) = $008kWh for gasoline Gasoline is cheap in the USA13

Examples13bull  Power vs Energy (P=Etime E = P t t = EP)13

ndash  Car goes 60 miles in one hour and uses 3 gal of gas What was total power in Watts P=Et Power = (3 gal1 hour) = 3galhr (366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W [Alternative method 3 galhr (132000000 J1 gal) (1 hr3600 sec) = 110000 Jsec = 110000 W13

ndash  1000 W space heater is on for 3 hours How much does it cost if electricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr (1kW1000W) = 3kWh ($15kWh) = $45 [Alternative method E = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000 J (1 kWh3600000J) = 3 kWh Again 45 cents13

ndash  AAA Battery contains 33 Calories of chemical energy How long can it run a 2 Watt light bulb time = EP time = 33 Calories2 W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1 hr3600 sec) = 19 hours13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

3813

Participation Questions13(write on piece of paper with name and hand in)13

The US uses about 7 Gbarrels of oil each year This could be converted into which of the following units13

A Joules13 B Watts13 C QBtus13 D Dollars $13 E Any of the above13

Participation Question13If one barrel of oil contains 1700 kWh of energy how many Watts is 7 Gbarrelyear13

A 1400 GW (Giga Watts)13

B 14 GW13

C 11900 W13

D 119 MW13

E 1 x 1011 W13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

3913

Participation Question13If the total yearly oil use in the US is about 1400 GW how many 1000 MW nuclear reactors will need to be built to replace all oil use with electricity13

A A little more than one will be needed13

B Around 1413

C Around 14013

D Around 140013

E Cant convert Watts to reactors power vs energy13

More Power Examples13bull  How much power does it take to lift 10 kg up 2 meters in 2

seconds13mgh = (10 kg)times(10 ms2)times(2 m) = 200J1313 13200 J in 2 seconds rarr 100 Watts13

bull  If you want to heat the 3 m cubic room by 10ordmC with a 1000 W space heater how long will it take1313We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes13

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13

4013

A note on arithmetic of units13bull  You should carry units in your calculations and multiply and divide them

as if they were numbers13bull  Example the force of air drag is given by13bull  13 13 Fdrag = frac12cDrAv213bull  cD is a dimensionless drag coefficient13bull  r is the density of air 13 kgm313bull  A is the cross-sectional area of the body in m213bull  v is the velocity in ms13bull  units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = 13

=

ENERGY CONVERSION FACTORS13bull  1kWh = 862 Cal = 3413 Btu = 36 MJ13bull  1 Cal = 0016 kWh = 397 Btu = 4184 J13bull  1 Btu = 252 Cal = 000293 kWh = 1055 J13bull  1 ft-lb = 136 J13bull  1 gal gasoline = 31000 Cal = 366 kWh =125000 Btu = 132 MJ13bull  1 bbl oil = 15M Cal = 58 M Btu = 1700 kWh =61 GJ13bull  1000 cf nat gas = 260000 Cal = 1M Btu = 300 kWh= 1GJ = 10 therm13bull  1 ton coal = 67M Cal = 27 M Btu = 7800 kWh = 28GJ13bull  1 Qbtu = 300 G kWh = 17 G boe13bull  POWER = ENERGYTIME CONVERSIONS13bull  100 Qbtuyr = 335 TW = 172 G boeyear13bull  1 Calhr = 116 W = 397 Btuhr13bull  1 horsepower = 746W = 550 ft-lbsec13bull  boe = barrel of oil equivalent Cal = kcal = 1000 cal J=Joule (metric)

kWh = kilo Watt hr W = Watt (metric)13bull  k=kilo M=Mega=106 G=Giga=109 T=Tera=1012

P=Peta=Q=Quadrillion=1015 13