Thermal Physics

HEAT AND TEMPERATURE

Temperature

Temperature: A measure of how hot (or cold) something isSpecifically, a measure of the average kinetic energy of the particles in an object.

If two objects of different temperatures are place in contact with one another, heat will “flow” from the high temp object to the low temp object.

Temperature is a property that determines the direction of thermal energy transfer between two bodies in thermal contact.

This flow of thermal energy will continue until the system reaches thermal equilibrium.

Concept Check

What is the relationship between the temperature of a substance and the speed of its molecules?

High temperature = _____ KE (high or low)?

Thermometers

Thermometer: an instrument that measures and indicates temperature

Bimetallic strip

a. b.

c.

Temperature Scales

KelvinInternational System (SI) of measurement

Fahrenheit

Celsius

Rankine

Newton

Romer scale

Kelvin and Absolute ZeroThe Kelvin scale is based on absolute zero

Absolute Zero: the temp at which molecular movement stops0 K on the Kelvin scale = -273.16ºC

It is the lowest temperature that can be theoretically achieved.

Scottish physicist William Thomson (a.k.a. Lord Kelvin) in 1848

Absolute Zero

Temperatures expressed by the Fahrenheit scale can be converted to the Celsius scale equivalent using the equation below:

°C = (°F - 32°)/1.8

Similarly, temperatures expressed by the Celsius scale can be converted to the Fahrenheit scale equivalent using the equation below:

°F= 1.8•°C + 32°

What is heat?

Heat: the transfer of energy between objects that are at different temperatures.

All matter has heat.

Measured in JOULES

Measuring Heat Flow

Two Common UnitsJoule

calorie

4.184 J = 1 cal

1Calorie = 1 kilocal = 1000 cal

Heating and Cooling

If an object has become hotter, it means that it has gained heat energy.

If an object cools down, it means it has lost energy

Endothermic and Exothermic Processes

Endothermic Process – heat is absorbed from the surroundings

Endo = Into

HEAT

Endothermic and Exothermic Processes

Exothermic process – heat is released into the surroundings

Exo = Exit

HEAT

Heating and Cooling cont…

Heat energy always moves from:

HOT object COOLER object

ex1. Cup of water at 20 °C in a room at 30°C - gains heat energy and heats up – its temperature rises

ex2. Cup of water at 20 °C in a room at 10°C loses heat energy and cools down – its temperature will fall.

ARE HEAT AND TEMP THE SAME THING?

NO….although the two quantities are related.Example: a beaker of water at 60 °C is hotter than a bath of water at 40 °C BUT the bath contains more joules of heat energy

Review

What is the difference between heat and temperature?

HEAT is energy that transfers from one object/substance to another

TEMPERATURE is a measure of the amount of energy an object/substance has (how quickly the molecules are moving around)

Internal energyInternal energy is the total potential energy and random kinetic energy of the molecules of the substance.

Microscopic scale, temp is the average kinetic energy per molecule associated with thermal motions.

aka: the faster the molecule are vibrating or moving inside an object the more internal energy it possesses.

Two rocks in an oven.Same heat input, different temperature rise.

Internal energy = total potential + total kinetic

Copper Phases – Vapor (gas)

Three Phases

Copper Phases - Solid

Copper Phases - Liquid

Copper Phases – Vapor (gas)

Measuring Heat Flow

Two Common UnitsJoule

calorie

4.184 J = 1 cal

1Calorie = 1 kilocal = 1000 cal

Concept Check

What causes heat to flow?

Energy Transfer

The transfer of heat is normally from a high temperature object to a lower temperature object.

1) Conduction

Thermal Conduction: the transfer of heat within a substance, molecule by molecule.

2) Convection

Convection: the movement of matter due to the differences in density that are caused by temp. variations applet

3) Radiation

Radiation: the energy that is transferred as electromagnetic waves, Doesn’t need matter

Most radiation comes from the sun

Conductor vs. Insulator

Conductor: any material through which energy can be transferred as heat

Insulator: poor conductors

Now to a mole!

Now to a mole!

Is a counting unit

The mole (mol) is the SI unit used to measure the amount of a substance.

It is based on the number of atoms in 12g of carbon

We can convert number of particles to moles and moles to particles.

The Mole

is 6.02 X 1023 (in scientific notation)

Similar to a dozen, except instead of 12, it’s 602 billion trillion 602,000,000,000,000,000,000,000

This number is named in honor of Amedeo Avogadro(1776-1856)

He studied quantities of gases and discovered that no matter what the gas was, there were the same number of molecules present

What is a mole?

One mole of anything consist of 6.02x1023 units of that substance.

How many eggs are in a mole of eggs?

How many paper clips are in a mole of paper clips?

How many shoes are in a mole of shoes?

Answer: 6.02x1023 eggs, paper clips, shoes

6.02 x 1023 particles

1 mole

or

1 mole

6.02 x 1023 particles

Note that a particle could be an atom, a molecule or anything!!!

Avogadro’s Number as Conversion Factor

Just How Big is a Mole?Enough soft drink cans to cover the surface of the earth to a depth of over 200 miles.

If you had Avogadro's number of unpopped popcorn kernels, and spread them across the United States of America, the country would be covered in popcorn to a depth of over 9 miles.

If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the atoms in one mole.

The Mole

This photograph shows one mole of salt(NaCl), water(H2O), and nitrogen gas(N2).

We also know…

1 mole of an elements atoms = that element’s average atomic mass (expressed in g)

We also know…

Ex. 200.6g of Hg has 6.02x1023 atoms or 200.6g of Hg has 1 mol of Hg atoms

Conversion factor: 200.6g Hg/1 mol Hg

Ex. 32.07g of S has 6.02x1023 atoms or 32.07g of S has 1 mol of S atoms

Conversion factor: 32.07g S/1 mol S

ExampleWe have an unknown # of H atoms.

We want to know many H atoms are present?

We weigh the sample, results = .5g

ExampleSo .5g H X (1mol H/1.008g H) = .496 mol of H in the sample.

Then .496 mol H atoms X (6.022x1023 H atoms/1 mol H atoms) = 2.99x1023 H atoms in the sample

Example

Convert 38g of P into moles of atoms

Convert 1.25 mol of Ag into # of atoms

Practice1. Convert 10g of Al into moles of atoms

2. Convert 8g of S into moles of atoms

3. Convert 25g of Ca into moles of atoms

4. Convert .371 mol Al into # of atoms

5. Convert .249 mol S into # of atoms

6. Convert .624 mol Ca into # of atoms

PracticeConvert .371 mol Al into # of atoms

Convert .249 mol S into # of atoms

Convert .624 mol Ca into # of atoms

Homework

8 moles F = ? grams F

4.2 moles Si = ? grams Si

9.3 moles Mg = ? grams Mg

945,000 Na atoms = ? moles Na

74,000 Cl atoms = ? Moles Cl

Summary1 amu = 1.66 x 10-24g

1 ___ atom = _____ amu1 C atom = 12.01 amu

1 Si atom = 28.09 amu

1 mol of ___ = 6.022x1023 ____ units1 mol F = 6.022x1023 F atom

1 mol Mg = 6.022x1023 Mg atom

What are the conversion factors?

Summary1mol of ___ = “atomic/molar mass” g of _____

1mol Hg = 200.6g Hg

1mol Cl = 35.45g Cl

“Atomic/molar mass” g of __ = 6.022x1023 atoms of ___200.6g Hg = 6.022x1023 atoms Hg

35.45g Cl = 6.022x1023 atoms Cl

What are the conversion factors?

ClassworkHow many moles are in 15 grams of lithium? How many atoms?

How many grams are in 2.4 moles of sulfur? How many atoms?

How many moles are in 22 grams of argon? How many atoms?

ClassworkHow many grams are in 88.1 moles of magnesium? How many atoms?

How many moles are in 2.3 grams of phosphorus? How many atoms?

How many grams are in 11.9 moles of chromium? How many atoms?

Molar Mass

Molar MassChemical compounds have multiple parts like the sucker.

Ex. Methane (natural gas) CH4

1 CH4 molecule

With 5 parts (1 C atom and 4 H atoms)

Quick NoteIn 1 mol of a molecule there are corresponding moles of its parts.

Ex. In 1 mol of CH4 there are 1 mol of C and 4 mol of H

Molar MassHow do we figure out the mass of 1 mol of methane?

We break it down in to its parts and add them up. This is called the molar mass.

Molar Mass- is the mass of a molecule Total mass of all the parts of a molecule

Example: SO2

What is the molar mass of SO2?

Mass of 1 mol of S = 1 x 32.07 = 32.07g

Mass of 1 mol of O = 2 x 16.00 = 32.00g

Mass of 1 mol of SO2 = 64.07g

The molar mass of SO2 is 64.07g

Example: CaCO3

What is the molar mass of CaCO3?

Mass of 1 mol of Ca = 1 x ____ = ____

Mass of 1 mol of C = 1 x _____ = ____

Mass of 1 mol of O = 3 x _____ = ____

Mass of 1 mol of CaCO3= ____

The molar mass of CaCO3 is _____

PracticeWhat is the molar mass of water, H2O?

What is the molar mass of ammonia, NH3?

What is the molar mass of propane, C3H8?

What is the molar mass and name of CaSO4?

What is the molar mass and name of Na2CO3?

What is the molar mass and name of Ba(OH)2?

PracticeWhat is the molar mass of water, H2O?

What is the molar mass of ammonia, NH3?

What is the molar mass of propane, C3H8?

PracticeWhat is the molar mass and name of CaSO4?

What is the molar mass and name of Na2CO3?

What is the molar mass and name of Ba(OH)2?

PracticeHow many molecules of water, H2O are in 100g?

How many grams of ammonia, are in 3.2 moles of NH3?

How many moles are in 400g of of propane, C3H8?

Thermal Capacity

Of a particular body is the energy required to raise the temperature of that body by 1°C.

Thermal capacity = change in thermal energy

temperature change

C = ∆Q / ∆T

Example 1

A 2 kg cylinder of copper is heated from room temperature (20˚C) to 500ºC. 374kJ of thermal energy were transferred to the copper during the heating process. Calculate the thermal capacity of this piece of copper.

Answer: 780J

Example 2

A 25kg cylinder of copper is heated from room temerature. The same 374kJ of thermal energy were used during the heating process but this time the copper’s temperature rose from room temperature to only 58.4ºC. Calculate the heat capacity of this piece of copper.

Answer: 9740J What is the difference between Ex 1 and Ex2

Specific HeatAdding energy to a material causes the temperature to go up.

Taking energy away from a substance causes the temp. to go down!

Have you ever noticed that on a hot summer day the pool is cooler than the hot cement?

OR maybe that the ocean is cooler than the hot sand?

Why? The sun has been beating down on both of them for the same amount of time...........

It takes more thermal energy to raise the temperature of water that it does the cement!

Water absorbs a lot of heat energy before its temperature changes while sand needs little heat energy before its temperature increases.

Specific HeatThe amount of energy required to raise the temperature of a material (substance).

It takes different amts of energy to make the same temp change in different substances.

We call the amt required: Specific Heat!

The specific heat capacity of a particular substance is equal to the energy required to raise the temperature of a 1kg mass of the substance by 1ºC

Specific Heat of water

The Cp is high because H2O mols. form strong bonds w/each other.

It takes a lot of energy to break the bonds so that the the molecules can then start to move around faster (HEAT UP).

Example:Specific Heat of

WaterCp = 4,184 Joules of energy to raise the temperature of 1kg 1°C.

video clipWhy Cp?

Cp Stands for “Heat Capacity”

Calculating Specific Heat

The Greek letter Δ means “change in”

EXAMPLE : p162Mass = 45kg

Q = 203,000J

Δt = 40°-28°

Δt = 12°

Cp = ?

Q =m x Cp x Δt

Q/(m x Δt) = Cp

Cp = 376 J/(kg °C)

Example 3

A 2kg cylinder of copper is heated from room temperature(20ºC) to 500ºC. 374kJ of thermal energy were transferred to the copper during the heating process. Calculate the specific heat capacity of this piece of copper.

Answer: 390J

Example 4

A 25kg cylinder of copper is heated from room temerature. The same 374kJ of thermal energy were used during the heating process but this time the copper’s temperature rose from room temperature to only 58.4ºC. Calculate the specific heat capacity of this piece of copper.

Answer: 390J

Solving for specific heatThere are two methods common for measuring the specific heat capacity.

Electrical – If an electrical immersion heater is place into a solid or a liquid, then the energy from the heater will be transmitted by conduction into the substance and the substance will get hotter.

Mixtures – If a hot object is place next to a cooler one (or placed into it if the cooler one is liquid), then the cooler substance will gain energy and become hotter and the hotter object will lose energy and become cooler until both objects come to the same temperature called thermal equilibrium.

Substance:WoodMercuryAlcoholWater (Ice)Water (Liquid)Water (Steam)

Specific Heat Capacity

17001402400210042002010

Example 5 – electrical A 240V electric heating element is used to heat water. The temperature of the water rose from 20ºC to 50ºC in 4minutes 20 seconds. During the heating process, the current flowing in the heater was measured to be 3.54A. Calculate the mass of the water.

Solution

First the power rating is Power = Voltage x Current

P = V I (I.B. Data booklet page 7)

P = 240 x 3.54 = 850W

The heater supplies 850J of energy to the water every second (850W= 850J/s). So in 4minutes 20seconds(260s), energy transferred to the water = 850 x 260 = 221x103J.

Answer: 1.75kg

Example 6The 850W heater was then placed into a hole in a piece of copper of mass 1.75kg. (A) Calculate the temperature rise in the copper if the heater was left on for 4min 20sec. (B) Calculate the final temperature of the copper if the heater was left on for 10min and the copper was originally at a temperature of 65ºC.

Answer: (A) = 324ºC, (B) = 812ºC

Example 7 – Mixture

A block of substance “X” has a mass of 100g and is heated to 260ºC. The block is then placed into a beaker containing 500g of water at 20ºC. After some time both substances reach their equilibrium temperature of 30ºC. Calculate the specific heat capacity of substance X.

Solution: Energy gained by the water = Energy lost by X

Qw = Qx

mwcw∆Tw = mxcx∆Tx

Answer = cx = 913J/kgºC

Example 8

How much energy is needed to heat a 1kg aluminum pan containing 2kg of water from 25ºC to 95ºC?

Solution: Total Energy = Energy gained by aluminum + Energy gained by water

Answer 651kJ

Example 9A 0.5kg block of copper (specific heat capacity 390J/kgºC) at an initial temperature of 420ºC was placed into 1.3kg of water at 40ºC. What will be the final temperature of the mixture when thermal equilibrium is reached?

Answer: Tfinal = 53.1ºC

Micro Properties of different phases

SolidsStrong bonds between atoms

Lowest internal energy

Atoms in fixed positions vibrating/oscillating

LiquidsWeaker forces. Some bonds are broken

More internal energy

Atoms can move about and change places

GasesVirtually no forces/bonds

High internal energy

Atoms completely free to move at high speed

Macro Properties of different phases

SolidsMaintain shape

Lowest temp

Low compression/expansion

LiquidsTakes the shape of its container

Moderate temp

Low compression/expansion

GasesFills the container

Highest temp

High compression/expansion

Plasmas – atoms are at extremely high temperatures and are ionized.

Usually found in stars.

Boiling causes evaporation.

Can a liquid evaporate with out boiling?

Evaporation vs Boilingin fluids

Molecules’ movement is completely random

Some high, some low.

As collisions occur, energy transfers from one molecule to another.

Eventually the kinetic energy > intermolecular binding energy

The individual molecules can break free from the surface.

Phase Change

Solid substance is heated

Gains thermal energy(kinetic) and molecular thermal motion

Average molecular thermal energy becomes the same as the intermolecular binding energies, a phase change occurs.

Crystal lattice can be broken and the solid melts.

This is the MELTING POINT!

Phase Change Detailed

Once the temp. has reached the melting point, the thermal energy is used to break bonds.

Substance gains potential energy, not kinetic.

Meaning no rise in temperature until all the substance has melted.

This can be applied to:liquids turning into gas

Gas turning into liquids

Liquids turning into solids

Lets look at what happens at each jump/step.

Latent Heat

Latent heat is the energy absorbed during a phase change.It does not increase the kinetic energy of the substanceAssociated with no temperature rise. Increases the potential energy

Latent heat of fusionSolid to liquid

Latent heat of vaporizationLiquid to gas

Latent Heat Formula

Specific latent heat = change in thermal energy

mass

L = ∆Q / m

Unit is J/kg or J kg- -1

Data book: ∆Q = mL

Example 10

Calculate the total energy that must be transferred to a 0.5kg block of ice at -12ºC if it is to be completely converted into 0.5kg of steam at 108ºC.

Answer: QT = 1525640J = 1.53MJ

Solution: This is essentially 5 separate calculations.

The 5 steps are the steps from: 1. A – B

2. B – C

3. C – D

4. D – E

5. E – F

Step one

The energy required to raise the temperature of the ice from –12ºC to 0ºC

Q1 = mIcI∆TI

Q1 = 0.5 x 2100 x 12

Q1 = 12600J

Step two

The energy required to melt the ice (at 0ºC)

Q2 = mI LF

Q2 = 0.5 x (3.3x105)

Q2 = 165000J

Practice 1

Calculate the total energy that must be transferred to a 5kg block of ice at -7ºC if it is to be completely converted into 5kg of steam at 104ºC.

Specific Latent HeatWe can find specific latent heats of fusion and vaporization of a substance by using the mixture and electrical methods as well.

Mixture Method

Lump of ice is dropped into waterThermal energy transferred to ice.

Temp of ice increases until it starts to melt @ 0ºC

Energy then goes into breaking bonds.

Once all ice has melted, the temp of liquid will rise.

A calorimeter with known specific heat and mass is usually used because the container’s temp will also drop the the same equilibrium temp. Calculations should be adjusted to incorporate the cooling of the container.

Example 11

50g of ice 0ºC is dropped into a beaker containing 200g of water initially at 30ºC. If the final temperature of the mixture is 10.2ºC, calculate the specific latent heat of fusion of ice.

Solution:

Energy from the water = Energy to the ice

The energy to the ice, is in two stages though. The first stage is in the melting the ice at 0ºC, the second is in raising the temp of the ice from 0ºC to 10.2ºC.

Answer: without calorimeter = 289800Jkg -1, with calorimeter = 312966Jkg -1.

Specific Latent HeatWe can find specific latent heats of fusion and vaporization of a substance by using the mixture and electrical methods as well.

Electrical Method – similar ideaElectric heating element is put in water

Temp of water will rise as thermal energy is absorbed

Once temp is 100ºC energy goes to breaking bonds

Mass of water will go down as the stem leaves the container

Specific latent heat of vaporization for water can then be calculated by examining the loss of mass and the energy input to the water.

Example 12

3kg of water at 20ºC were put into an electric kettle with a power rating of 2kW and heated until it boiled. Once boiling the kettle continued to transfer thermal energy to the water for a further 6 min. The mass of the water after this time was seen to drop to 2. 68kg. Calculate the specific latent heat of vaporization for water.

Solution

Energy from the kettle to the water = power x time

∆Q = mL

Example 131.5 kg of water at 25ºC were put into an electric kettle with a power rating of 2.5kW and heated. Calculate the time taken to boil the water off completely. (i.e. all the water turned into steam).

Solution:

Energy needed = Energy to raise temp to 100ºC + Energy to convert water to steam

∆Q = 3.86 x 106

The kettle supplies 2500J of energy every second

T = ∆Q / P

Pressure

Gas molecule movement is random. (speed/direction)

Collisions occur all the time. (molecules/container)

Pressure is the result of these collisions.

On a microscopic scale, pressure is the result of the force imparted on the area of a container wall due to the change in momentum of the colliding molecules.

Pressure = Force / Surface Area

p = F/A

Kinetic model of an ideal gas

Uses the microscopic (atomic) model to explain the macroscopic (bulk) properties of gasses, particularly pressure and absolute temperature.

The pressure exerted on the inner wall of the container is due to the constant collisions between the molecules and the inner wall.

More collisions = higher pressure

Kinetic model of an ideal gas1) There are large numbers of molecules, N, each of

mass, m, moving with random velocities (both speed and direction).

2) The molecules are far apart from one another. That is, their average separation is much greater than their diameter.

3) The forces of attraction between the molecules are so small that they can be ignored.

4) The molecules obey the laws of classical mechanics and interact with one another only when they collide.

5) Collisions between molecules or with the wall of the container are perfectly elastic i.e. momentum and kinetic energy is conserved during the collision.

Equations

PV = nRT

Pressure x Volume = number of moles x constant x Temp

R= 8.31J/K mol

(Pressure)(volume)/(mol)(Temp) = (Pressure)(Volume)/(mol)(Temp)

P1 V1 = P2V2

n1 T1 n2T2

Summarized

If volume is ½ed, then molecules are closer together and therefor have twice as many collisions. Also, twice the collisions means double the pressure.

If volume is constant, and temp is increased, then pressure will increase.

Example 14

How many moles of gas are there in a gas of temp 300K, volume .02m3 and pressure of 2 x105 Pa.

Answer: 1.6mol

Example 15

A container of hydrogen of volume 0.1 m3 and temp of 25ºC contains 3.2x1023 molecules. What is the pressure in the container?

Answer:

Number of moles = .53

P = 1.3 x 104 Nm-2

Example 16

A gas of volume 2L, pressure 3atm and temp 300K expands to a volume of 3 L and a pressure of 4 atm. What is the new temperature of the gas?

Answer:

PV/RT = n

PV/RT = PV/RT

PV/T = PV/T

T= 600K

A by traveling through space as wavesB by the movement of fluidsC by the expansion of gasesD by contact between particles

Conduction can BEST be described as the transfer of

energy

A copper ornament has a

mass of 0.0693 kg and changes from a temperature of 20.0°C to 27.4ºC. How much heat

energy did it gain?