temperature thermal expansion ideal gas law heat transfer...
TRANSCRIPT
•Temperature
•Thermal Expansion
•Ideal Gas Law
•Kinetic Theory
•Heat
•Heat Transfer
•Phase Changes
•Specific Heat
•Calorimetry
Zeroeth Law
• Two systems individually in thermal
equilibrium with a third system (such as a
thermometer) are in thermal equilibrium
with each other.
• That is, there is no flow of heat within a
system in thermal equilibrium
1st Law of Thermo
• The change of internal energy of a system
due to a temperature or phase change is
given by (next chapter):
Temperature Change: Q = mcT
Phase Change: Q = mL
• Q is positive when the system GAINS heat
and negative when it LOSES heat.
2nd Law of Thermo
• Heat flows spontaneously from a substance
at a higher temperature to a substance at a
lower temperature and does not flow
spontaneously in the reverse direction.
• Heat flows from hot to cold.
• Alternative: Irreversible processes must
have an increase in Entropy; Reversible
processes have no change in Entropy.
• Entropy is a measure of disorder in a system
3rd Law of Thermo
It is not possible to
lower the
temperature of any
system to absolute
zero.
9( ) ( ) 32
5T F T C
5( ) ( ) 32
9T C T F
( ) ( ) 273.15T K T C
Temperature is measured by a thermometer.
Kelvin is the Absolute Scale.
What is "room temperature" (68 degrees F) in Celsius and Kelvin?
5( ) ( ) 32
9T C T F
( ) ( ) 273.15T K T C
568 32
9 20 C
293.15K
Do book quiz 2!
30 is HOT.
20 is NICE.
10 is CHILLY.
Zero is ICE!
Thermal Expansion of Solids: Linear
0L L T
Coefficients determined experimentally!
Thermal Expansion: Volume
0V V T
~ 3
Thermal Expansion: Linear
Thermal Expansion: Linear
The coefficient of linear expansion of steel is 12 x 10-6/°C.
A railroad track is made of individual rails of steel 1.0 km in length.
By what length would these rails change between
a cold day when the temperature is -10 °C and a hot day at 30 °C?
6 3(12 10 / )(10 )(30 ( 10 ))L x C m C C
.48L m
0L L T
What change in temperature is needed to fill the gap, 1.3 x 10 -3 m?
6 0 1 6 0 119 10 23 10 brass ALx C x C
0L L T
31.3 10brass AlL L x m
31.3 1011
brass brass Al Al
x mT C
L L
21
Thermal Expansion
When the temperature of a metal ring increases,
does the hole become larger?
Smaller? Or stay same?
Circle Expansion
The coefficient of linear
expansion of aluminum is
23 x 10-6/C°. A circular
hole in an aluminum plate is
2.725 cm in diameter at 0°C.
What is the diameter of the
hole if the temperature of
the plate is raised to 100°C?
0L L T 6(23 10 / )(2.725 )100x C cm C
2.731d cm36.3 10x cm
Fluids: Liquids & Gases
•Fluids are substances that are free to flow.
•Atoms and molecules are free to move.
•They take the shape of their containers.
•Cannot withstand or exert shearing forces.
Liquids: Incompressible (density constant)
Gases: Compressible (density depends on pressure)
Parameters to describe Fluids:
Density: = mass/volume
Pressure: P = Force/Area
[P] = N/m2 = 1 Pascal (Pa)
Liquid Units
There are 1000 liters in 1 cubic meter!
1 liter = 10-3 m3 = 103 cm3
1 liter of water has a mass of 1 kg and a weight of 9.8N.
2 0 3
1 1000H
kg kg
liter m
Density • Density of water @4°C:
water = 1g/cm3 = 1000 kg/m3 = 1kg/liter
• Density of air @ 0°C:
Air = 1.29x10-3 g/cm3 = 1.29 kg/m3
Density depends on temperature! Most substances EXPAND upon heating.
m
V
How does that change their densities?
REDUCES DENSITY! m
V
m V
Water: The Exception
• Water @4°C: water =1000 kg/m3
• Ice @ 0°C: ice = 917 kg/m3
Increasing the Pressure
Does increasing the external pressure increase
or decrease the boiling temperature of water?
Increases! Boiling happens when vapor pressure in the
liquid exceeds the external vapor pressure - now greater
due to the increased pressure – so the boiling temperature
increases!
n = # moles
R = 8.31 J/(mol-K) Universal Gas Constant
The absolute Pressure P of an ideal gas is directly proportional to
the absolute (Kelvin) temperature T and the number of moles n of
the gas and inversely proportional to the volume V of the gas:
P V = nRT
Thermometer, Liquid in Glass
• A common type of
thermometer is a
liquid-in-glass
• The material in the
capillary tube
expands as it is
heated
• The liquid is
usually mercury or
alcohol
10.3m
Mercury Barometer Water Barometer
Not to Scale!!!
51 1.013 10atm x Pa 760mm
Barometers
Measuring Air Pressure Fluid in the tube adjusts until the weight of the fluid column
balances the atmospheric force exerted on the reservoir.
The Atmosphere
At sea level,
the atmosphere
has a density of
about 1.29 kg/m3.
The average
density up to
120 km is about
8.59 x10-2 kg/m3.
The Atmosphere
A square meter
extending up through
the atmosphere has a
mass of about
10,000 kg and a weight
of about 100,000 N.
1 N/m2 is a Pascal.
51 1.013 10 14.7atm x Pa psi
Pressure in a fluid is due to the weight
of a fluid. Force
PArea
mg
A
Pressure depends on Depth!
( )V g
A
( )Ah g
A
P gh
Measuring Pressure 51 1.013 10atm x Pa
760h mm
13.6mercury water
mercuryP gh
mercury
Ph
g
2
3 2
101,300 /
13,600 / 9.8 /
N mh
kg m x m s
P gh
Why is the pressure at X equal to atmospheric pressure?
Because if it didn’t, the mercury would
be pushed out of the dish!
31000 /water kg m
Measuring Pressure
Can a barometer be made with Water instead of Mercury?
waterP gh
water
Ph
g
2
3 2
101,300 /
1000 / 9.8 /
N mh
kg m x m s
10.3h m
(Notice: 10.3m is just 13.6 x 760mm!)
13.6mercury water
31000 /water kg m
Absolute vs. Gauge Pressure
• Guage pressure is
what you measure in
your tires
• Absoulte pressure is
the pressure at B and
is what is used in
PV = nRT
0Guage Pressure: P gh
0Absolute Pressure: P P gh
n = # moles
R = 8.31 J/(mol-K) Universal Gas Constant
Note: PV is units of Energy!
P V = nRT
•Atomic Number: # protons
•Atomic Mass: # atomic mass units (u)
•Atomic Mass Unit: 1/12 mass of C-12 atom
• amu = u = 1.66 x 10-27 kg
•Atomic Mass of C = 12.011u (1% is C-13)
•Mass of 1 C = (12.011u) (1.66 x 10-27 kg/u)
Atomic Units
The Basics
•Mole (mol) = # atoms or molecules (particles) as
are in 12 grams of Carbon-12:
1 mole = 6.022 x 1023 particles
• Avogadro’s Number: the number of particles in
one mole: NA= 6.022 x 1023 mol-1
•# moles n contained in a sample of N particles:
n = N/ NA
• # particles in a sample is: N = n NA
Moles and Avogadro’s Number NA= 6.022 x 1023 mol-1
The mass / mol for any substance
has the same numerical value
as its atomic mass:
mass/mol C-12 = 12 g / mol
mass/mol Li = 6.941 g / mol
More on Moles
n = mass / atomic mass
n = mass / (mass/mole) = mass / atomic mass
Q: How many moles are in 1 kg of Sodium?
mass/mole = atomic mass
Na: 22.9898 g / mol
n = mass / (mass/mole)
= 1000 g / (22.9898g/mol)
= 43.5 moles
Q: How many atoms in 1 kg of Sodium?
# particles in a sample is: N = n NA
N = (43.5mol) 6.022 x 1023 mol-1
= 2.62 x 1025 atoms
n = # moles
R = 8.31 J/(mol-K) Universal Gas Constant
PV = Nkt N= # particles
k =1.38 x 10-23 J/K Boltzmann’s Constant
Note: PV is units of Energy!
P V = nRT
• The only interaction between particles are
elastic collisions (no sticky - no loss of KE)
• This requires LOW DENSITY
• Excellent Approximation for O, N, Ar, CO2
@ room temperature and pressures
• “State” is described by the Ideal Gas Law
• Non “Ideal” are Van der Waals gases
Ideal Gas Problem An ideal gas with a fixed number of molecules
is maintained at a constant pressure. At 30.0
°C, the volume of the gas is 1.50 m3. What is
the volume of the gas when the temperature is
increased to 75.0 °C?
1 1PV nRT
2 2PV nRT
1 1
2 2
V T
V T
22 1
1
TV V
T 3 3348
1.5 1.72303
Km m
K
•Heat flows from HOT to COLD
•Conduction (solids)
•Convection (liquids & gases)
•Radiation (solids, gases, plasma)
Energy transferred via molecular collisions
•Good Conductors: Most Metals (free
electrons!)
•Bad Conductors: Organic & Inert
Materials
•Good Insulators: Air, Water, Wood
•Good Conductors are BAD Insulators
•& Visa Versa
Heat energy is transferred in solids
by collisions between free electrons
and vibrating atoms.
The heat Q conducted during a time t through a material with
a thermal conductivity k. dT/dx is the Temperature Gradient.
dTP kA
dx
Some Thermal Conductivities
Temperature Gradient
h cdT T T
dx L
The quantity |dT / dx| is called the temperature gradient
Q dTkA
t dx
Compound Slab: R values
h c
i i
i
A T T
L k
• For a compound slab containing several
materials of various thicknesses (L1, L2, …) and
various thermal conductivities (k1, k2, …) the
rate of energy transfer depends on the materials
and the temperatures at the outer edges:
• Substances are rated by their R values
– R = L / k and the rate becomes
– For multiple layers, the total R value is the sum of the R values of each layer
• Wind increases the energy loss by conduction in a home
h c
i
i
A T T
R
Conduction Problem
A bar of gold is in thermal contact with a bar of silver of the
same length and area as shown. One end of the compound
bar is maintained at 80.0°C while the opposite end is at
30.0°C. When the energy transfer reaches steady state, what
is the temperature at the junction? Ignore thermal
expansion of the metals.
h cT TkA
L
In the same room, at the same
temperature, the tile floor feels
cooler than wood floor.
How can they be the same
temperature?
Hot Air rises, expands and cools, and then sinks back down
causing convection currents that transport heat energy.
Hot air rises because fast moving molecules tend to migrate toward
regions of least obstruction - UP - into regions of lesser density!
Rising air cools because a decrease in density
reduces number of collisions & speeds decrease.
As the air cools, it becomes denser, sinking down,
producing a convection current.
Uneven heating on the earth and over water cause convection
currents in the atmosphere, resulting in WINDS.
Global wind patterns (Trade Winds, Jet Streams) are due to
convection current from warmer regions (equator) to cooler
regions (poles) plus rotation of Earth.
Convection Currents in the Ocean (Gulf Stream)
transport energy throughout the oceans.
Air & Ocean Convection causes
the WEATHER.
Convection between water and land causes the Winds.
Sea Breeze
High Pressure
Dry Warm Weather
Low Pressure
Stormy Weather
Electromagnetic Radiation is emitted and absorbed via atomic
excitations. All objects absorb and emit EM waves.
Electromagnetic Radiation is emitted and absorbed via atomic
excitations. All objects absorb and emit EM waves.
When an object it heated it will
glow first in the infrared, then the
visible. Most solid materials break
down before they emit UV and
higher frequency EM waves.
Frequency ~ Temperature
Long
Short
Stefan’s Law
• P = σAeT 4
– P is the rate of energy transfer, in Watts
– σ = 5.6696 x 10-8 W/m2 . K4
– A is the surface area of the object
– e is a constant called the emissivity
• e varies from 0 to 1
• The emissivity is also equal to the absorptivity
– T is the temperature in Kelvins
A good absorber reflects little and appears Black
A good absorber is also a good emitter.
4P e T A
Radiant heat makes it impossible to stand close to a hot
lava flow. Calculate the rate of heat loss by radiation
from 1.00 m2 of 1200C fresh lava into 30.0C
surroundings, assuming lava’s emissivity is 1.
The net heat transfer by radiation is: 4 4
2 1( )P e A T T
4 4
2 1( )P e A T T
8 4 2 4 41(5.67 10 / )1 ((303.15 ) (1473.15 ) )x J smK m K K
266P kW
Fur is filled with air. Convection currents are slow
because the convection loops are so small.
How do fur coats keep you warm?