Thermal Physics
AP Physics BLecture Notes
x
z
Thermal Physics
10-01 Temperature and the zeroth Law of Thermodynamics
10-02 Thermometers and Temperature Scales
10-03 Thermal Expansion of Solids and Liquids
10-04 Microscopic Description of an Ideal Gas
Topics
10-05 The Kinetic Theory of Gases
Temperature and the zeroth Law of Thermodynamics
Two objects placed in thermal contact will eventually come to the same temperature. When they do, we say they are in thermal equilibrium.
A B
C
Then A and B are in thermal equilibrium.
If A is in thermal equilibrium with Cand B is in thermal equilibrium with C
The Zeroth Law of Thermodynamics
Thermometers and Temperature Scales
Temperature is a measure of how hot or cold something is.
Thermometers are instruments designed to measure temperature. In order to do this, they take advantage of some property of matter that changes with temperature.
Most materials expand when heated.
Common thermometers used today include the liquid-in-glass type and the bimetallic strip.
Thermometers and Temperature Scales
Thermal Physics 10-01
A bimetallic strip, consisting of metal G on the top and metal H on the bottom, is rigidly attached to a wall at the left as shown. In the diagram. The coefficient of linear thermal expansion for metal G is greater than that of metal H. If the strip is uniformly heated, it will
(A) curve upward.
(B) curve downward.
(C) remain horizontal, but get longer.
(D) bend in the middle.
0 -273 -459
Celsius FahrenheitKelvin
273 0 32
373 100 212
Boiling
Point (H2O)
Melting
Point (H2O)
Absolute Zero
Temperature is generally measured using either the Kelvin, Celsius, or the Fahrenheit scale.
Thermometers and Temperature Scales
Thermal Expansion of Solids and Liquids
A steel washeris heated
Does the hole increase or decrease in size?
Expansion occurs when an object is heated.
When the washeris heated
The hole becomeslarger
Thermal Expansion of Solids and Liquids
Thermal Physics 10-02
Consider a flat steel plate with a hole through its center as shown in the diagram. When the plate's temperature is increased, the hole will
(A) expand only if it takes up more than half the plate's surface area.
(B) contract if it takes up less than half the plate's surface area.
(C) always contract.
(D) always expand.
LoL
L LoT
TL = LoT
L = Lo(1+T)
Coefficient oflinear expansion
L Lo = LoT
Thermal Expansion of Solids and Liquids
A cylindrical brass sleeve is to be shrunk-fitted over a brass shaft whose diameter is 3.212 cm at 0 oC. The diameter of the sleeve is 3.196 cm at 0 oC.
D d
To what temperature must the sleeve be heated before it will slip over the shaft?
shaft sleeve
Thermal Expansion of Solids and Liquids (Problem)
To what temperature must the sleeve be heated before it will slip over the shaft?
shaft sleeve
D d
C/1 10 x 19 o6
TLL i
ddD
Tf
C0T
cm 196.3dcm 212.3D
oi
cm 3.196C/1 10x 19
cm 3.196cm 3.212o6 C 263 o
dDL
if TTddD
fdTdD
Thermal Expansion of Solids and Liquids (Problem)
32o
2o
3o LLL3LL3LV
New Volume
3o LLV
Initial Volume
3oo LV
TL3V 3o
Lo
Lo
Lo
Lo + L
Lo + L
Lo + LVolume Expansion
L = LoT
LL3VVV 2oo
TLL3V o2o
TV3V o
Thermal Expansion of Solids and Liquids
TV3V o
3
TVV o
TVVV oo
T1VV o
Coefficientof
VolumeExpansion
Thermal Expansion of Solids and Liquids
An automobile fuel tank is filled to the brim with 45 L of gasoline at 10 oC. Immediately afterward, the vehicle is parked in the Sun, where the temperature is 35 oC. How much gasoline overflows from the tank as a result of expansion?
SG VVV
TVV oSG
2545 10 x 3310 x 6.9 V 64
L 04.1V
Overflow
Change in volumeof the gasoline
Change in volumeof the steelgas tank
TVTVV oSoG
Thermal Expansion of Solids and Liquids (Problem)
PV = nRT
Pressure(Pa)
Volume(m3)
AbsoluteTemperature
(K)
Gas Constant(8.31 J/molK)
0.0821 (L.atm)/(mol.K)
1.99 cal/(mol.K)
Gas Quantity(mol)
Microscopic Description of an Ideal Gas
Thermal Physics 10-03
~M1 ~M2 ~M3 ~M4 ~M5 ~M6 ~M7 ~M8 ~M10~M9~M11~M12~M13~M14~M15~M16~M17~M18 ~M20~M19~M21~M22~M23~M24~M25~M26~M27~M28 ~M30~M29~M31~M32~M33~M34~M35~M36~M37~M38 ~M40~M39~M41~M42~M43~M44~M45~M46~M47~M48 ~M50~M49~M51~M52~M53~M54~M55~M56~M57~M58 ~M60~M59
Both the pressure and volume of a given sample of an ideal gas double. This means that its temperature in Kelvin must
(A) double.
(B) quadruple.
(C) reduce to one-fourth its original value.
(D) remain unchanged.
A mole (mol) is defined as the number of grams of a substance that is numerically equal to the molecular mass of the substance:
1 mol H2 has a mass of 2 g1 mol Ne has a mass of 20 g1 mol CO2 has a mass of 44 g
mol/g mass molecular
grams massmol n Μ
mn
mol/particlesnumber svogadro'A)(particles molecules
mol n AN
Nn
The number of moles in a certain number of particles:
The number of moles in a certain mass of material:
Microscopic Description of an Ideal Gas
PV = NkT
Pressure(Pa)
Volume(m3)
AbsoluteTemperature
(K)
Boltzmann’sConstant
(1.38 x 10-23 J/K)
Number ofMolecules
Microscopic Description of an Ideal Gas
Boltzmann’s Constant
nRTPV NkT
NnR
k
nNR
k
GasConstant
Avogadro’sNumber
Microscopic Description of an Ideal Gas
A gas is contained in an 8.0 x 103 m3 vessel at 20 oC
and a pressure of 9.0 x 105 N/m2.
(a) Determine the number of moles of gas in the vessel.
nRTPV
RTPV
n K 293Kmol/J 31.8
m10 x 0.8N/m 10 x 0.9 2325
mol 0.3n
Microscopic Description of an Ideal Gas (Problem)
A gas is contained in an 8.0 x 103 m3 vessel at 20 oC
and a pressure of 9.0 x 105 N/m2.
(b) How many molecules are in the vessel?
AnNN
mol 0.3n
mol
molecules23 10 x 02.6mol 0.3
molecules 10 x 8.1N 24
Microscopic Description of an Ideal Gas (Problem (con’t))
Thermal Physics 10-04
A container of an ideal gas at 1 atm is compressed to one-third its volume, with the temperature held constant. What is its final pressure?
(A) 1/3 atm
(B) 1 atm
(C) 3 atm
(D) 9 atm
A cylinder with a moveable piston contains gas at a temperature of 27 oC, a volume
of 1.5 m3, and an absolute
pressure of 0.20 x 105 Pa.
1.5 m3
27 oC
0.20 x 105 Pa
0.70 m3
0.80 x 105 Pa
Microscopic Description of an Ideal Gas
What will be its final temperature
if the gas is compressed to 0.70 m3 and the absolute pressure increases
to 0.80 x 105 Pa? 1.5 m3
27 oC
0.20 x 105 Pa
0.70 m3
0.80 x 105 Pa
nRTPV constantnRT
PV
i
ii
f
ffTVP
TVP
ii
ffif VP
VPTT
35
35
m 5.1 Pa 10 x 2.0
m 7.0 Pa 10 x 8.0K 300 K 560
273
C 287 o
Microscopic Description of an Ideal Gas (Problem)
K 300C 27 o
The Kinetic Theory of Gases
Assumptions of kinetic theory:
2) molecules are far apart, on average
1) large number of molecules, moving in random directions with a variety of speeds
3) molecules obey laws of classical mechanics and interact only when colliding
4) collisions are perfectly elastic
x
y
z
v
L
AThe force exerted on the wall by the collision of one molecule of mass m is
tΔ
mvΔF
x
x
vL2mv2
L
mv2x
Then the average force due to N molecules colliding with that wall is
2xvN
Lm
F
The Kinetic Theory of Gases
The averages of the squares of the speeds in all three directions are equal:
So the pressure on the wall is:
AF
P AL
vNm 2
31
VvNm 2
31
LvmN
F2
31x
y
z
v
L
A
2xvN
Lm
F
The Kinetic Theory of Gases
Rewriting,
so
The average translational kinetic energy of the molecules in an ideal gas is directly proportional to the temperature of the gas.
221
32 vm NPV NkT
kTvm 221
32
kTvmEK 232
21
VvNm
P2
31
The Kinetic Theory of Gases
Molecular Kinetic Energy
Temperature is a measure of the averagemolecular kinetic energy.
2kT3
KE
mkT3
v rms
2vm 2
2kT3
2vm 2
The Kinetic Theory of Gases
Thermal Physics 10-05
According to the ideal gas Law, PV = constant for a given temperature. As a result, an increase in volume corresponds to a decrease in pressure. This happens because the molecules
(A) collide with each other more frequently.
(B) move slower on the average.
(C) strike the container wall less often.
(D) transfer less energy to the walls of the container each time they strike it.
Thermal Physics 10-06
The absolute temperature of an ideal gas is directly proportional to which of the following?
(A) speed
(B) momentum
(C) kinetic energy
(D) mass
Thermal Physics 10-07
Oxygen molecules are 16 times more massive than hydrogen molecules. At a given temperature, the average molecular kinetic energy of oxygen, compared to hydrogen
(A) is greater.
(B) is less.
(C) is the same.
(D) cannot be determined since pressure and volume are not given
What is the total random kinetic energy of all themolecules in one mole of hydrogen at a temperatureof 300 K.
kT
23
NK A
Avogadro’snumber
Kinetic energy per molecule
J 3740K
K 003 KJ
10 x 38.1 23
molecules 10 x 02.6K 2323
The Kinetic Theory of Gases (Problem)
Calculate the rms speed of a Nitrogen molecule (N2)
when the temperature is 100 oC.
Mass of N2 molecule:
kg 10 x .654 26
kg 10 x .654
K 373 J/K 10 x .381326
23
m
kT3v rms
m/s 576v rms
rms speed:
molemolecules/ 10 x .026
kg/mole 10 x 0.28m
23
3
The Kinetic Theory of Gases (Problem)
If 2.0 mol of an ideal gas are confined to a 5.0 L vessel at
a pressure of 8.0 x 105 Pa, what is the average kineticenergy of a gas molecule?
Temperature of the gas:
nRTPV
nRPV
T
KmolJ
31.8mol 0.2
m 10 x 0.5Pa 10 x 0.8
335K 442
Kinetic energy:
kT23
K K 244KJ
10 x 38.123 23
molecule
Jx 2110 05.5
The Kinetic Theory of Gases (Problem)
Thermal Physics 10-08
A container holds N molecules of an ideal gas at a given temperature. If the number of molecules in the container is increased to 2N with no change in temperature or volume, the pressure in the container
(A) doubles.
(B) remains constant.
(C) is cut in half.
(D) none of the above
Mean and rms Speed5
2
3
6 2
61
4Mean Speed:
852362461
8
52362461 22222222
rms Speed:
m/s 4.0v rms
m/s 3.6v mean
The Kinetic Theory of Gases
Thermal Physics 10-09
A sample of an ideal gas is slowly compressed to one-half its original volume with no change in temperature. What happens to the average speed of the molecules in the sample?
(A) It does not change.
(B) It doubles.
(C) It halves.
(D) none of the above
Thermal Physics 10-10
A mole of diatomic oxygen molecules and a mole of diatomic nitrogen molecules at STP have
(A) the same average molecular speeds.
(B) the same number of molecules.
(C) the same diffusion rates.
(D) all of the above
Summary
Temperature is a measure of how hot or cold something is, and is measured by thermometers.
There are three temperature scales in use: Celsius, Fahrenheit, and Kelvin.
When heated, a solid will get longer by a fraction given by the coefficient of linear expansion.
The fractional change in volume of gases, liquids, and solids is given by the coefficient of volume expansion.
nRTPV Ideal gas law:
One mole of a substance is the number of grams equal to the atomic or molecular mass.
Each mole contains Avogadro’s number of atoms or molecules.
The average kinetic energy of molecules in a gas is proportional to the temperature:
kTvmEK 232
21
Summary