Thermal Physics
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Physics 2053
Lecture Notes
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Thermal Physics (01 of 45)
Thermal Physics
Topics
10-01 Temperature and the zeroth Law of Thermodynamics
10-02
10-03
10-04
10-05
Thermometers and Temperature Scales
Thermal Expansion of Solids and Liquids
Microscopic Description of an Ideal Gas
The Kinetic Theory of Gases
Thermal Physics (02 of 45)
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.
The Zeroth Law of Thermodynamics
C
A
B
If A is in thermal equilibrium with C
and B is in thermal equilibrium with C
Then A and B are in thermal equilibrium.
Thermal Physics (03 of 45)
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.
Thermal Physics (04 of 45)
Thermometers and Temperature Scales
Common thermometers used today include the liquid-in-glass
type and the bimetallic strip.
Thermal Physics (05 of 45)
Thermometers and Temperature Scales
Temperature is generally measured using either the Kelvin,
Celsius, or the Fahrenheit scale.
Kelvin
Celsius
Fahrenheit
Boiling
Point (H2O)
373
100
Melting
Point (H2O)
273
0
32
0
-273
-459
Absolute Zero
212
Thermal Physics (07 of 45)
Thermal Expansion of Solids and Liquids
Expansion occurs when an
object is heated.
A steel washer
is heated
Does the hole increase
or decrease in size?
Thermal Physics (08 of 45)
Thermal Expansion of Solids and Liquids
When the washer
is heated
The hole
becomes
larger
Thermal Physics (09 of 45)
Thermal Physics 10
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.
Thermal Expansion of Solids and Liquids
∆L
Lo
∆L ∝ Lo∆T
∆T
∆L = αLo∆T
L − Lo = αLo∆T
Coefficient of
linear expansion
L = Lo(1+α∆
α∆T)
α∆
Thermal Physics (11 of 45)
Thermal Expansion of Solids and Liquids (Problem)
sleeve
shaft
D
d
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.
To what temperature must the sleeve be heated before
it will slip over the shaft?
Thermal Physics (12 of 45)
Thermal Expansion of Solids and Liquids (Problem)
shaft
sleeve
D
d
To what temperature must the sleeve be
heated before it will slip over the shaft?
α = 19 x 10 − 6 1 / o C
Thermal Physics (13 of 45)
Thermal Physics 10
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.
Thermal Expansion of Solids and Liquids
Volume Expansion
Lo
Lo
Lo + ∆L
Lo + ∆L
Lo + ∆L
Lo
New Volume
V = (Lo + ∆L )3
Initial Volume
Vo = L3o
V = L3o + 3L2o ∆L + 3Lo (∆L )2 + ∆L3
∆V = V − Vo = 3L2o ∆L
∆V = 3L2o (αL o ∆T )
∆V
= 3αL3o ∆T
∆L = αLo∆T
∆V = 3αVo ∆T
Thermal Physics (14 of 45)
Thermal Expansion of Solids and Liquids
∆V = 3αVo ∆T
β = 3α
Coefficient
of
Volume
Expansion
∆V = β Vo ∆T
V − Vo = β Vo ∆T
V = Vo (1 + β ∆T )
Thermal Physics (15 of 45)
Thermal Expansion of Solids and Liquids (Problem)
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?
Thermal Physics (16 of 45)
Potential Energy
Thermal Expansion of Solids and Liquids
High Temperature
Low Temperature
Intermolecular Distance
Thermal Physics (17 of 45)
Microscopic Description of an Ideal Gas
Pressure
(Pa)
Volume
(m3)
PV = nRT
Gas Quantity
(mol)
Absolute
Temperature
(K)
Gas Constant
(8.31 J/mol.K)
0.0821 (L.atm)/(mol.K)
1.99 cal/(mol.K)
Thermal Physics (18 of 45)
Thermal Physics 10
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.
Microscopic Description of an Ideal Gas
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 g
1 mol Ne has a mass of 20 g
1 mol CO2 has a mass of 44 g
The number of moles in a certain mass of material:
mass (grams )
n (mol ) =
molecular mass (g / mol )
m
⇒ n=
Μ
The number of moles in a certain number of particles:
molecules (particles)
n (mol ) =
Avogadro' s number (particles / mol )
⇒ n=
N
NA
Thermal Physics (20 of 45)
Microscopic Description of an Ideal Gas
Pressure
(Pa)
Volume
(m3)
PV = NkT
Number of
Molecules
Absolute
Temperature
(K)
Boltzmann’s
Constant
(1.38 x 10-23 J/K)
Thermal Physics (21 of 45)
Microscopic Description of an Ideal Gas
Boltzmann’s Constant
PV = nRT = NkT
nR
k=
N
R
k=
N
n
Gas
Constant
Avogadro’s
Number
Thermal Physics (22 of 45)
Microscopic Description of an Ideal Gas (Problem)
A gas is contained in an 8.0 x 10−3 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.
Thermal Physics (23 of 45)
Microscopic Description of an Ideal Gas (Problem (con’t))
A gas is contained in an 8.0 x 10−3 m3 vessel at 20 oC
and a pressure of 9.0 x 105 N/m2.
n = 3.0 mol
(b) How many molecules are in the vessel?
Thermal Physics (25 of 45)
Thermal Physics 10
A container of an ideal gas at 1 atm is compressed to onethird 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
Microscopic Description of an Ideal Gas
0.20 x 105 Pa
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
Thermal Physics (26 of 45)
Microscopic Description of an Ideal Gas (Problem)
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?
0.20 x 105 Pa
1.5 m3
27 oC
0.80 x 105 Pa
0.70 m3
Thermal Physics (27 of 45)
The Kinetic Theory of Gases
Assumptions of kinetic theory:
1) large number of molecules, moving in
random directions with a variety of speeds
2) molecules are far apart, on average
3) molecules obey laws of classical mechanics and
interact only when colliding
4) collisions are perfectly elastic
Thermal Physics (28 of 45)
The Kinetic Theory of Gases
y
v
The force exerted on the wall by the collision
of one molecule of mass m is
A
x
z
L
2
∆(mv )
2mv x
mv
x
F=
=
=
2L
∆t
L
vx
Then the average force due to N
molecules colliding with that wall is
F=
m
N v 2x
L
Thermal Physics (29 of 45)
The Kinetic Theory of Gases
y
v
The averages of the squares of the speeds
in all three directions are equal:
A
x
 mN v 2 
1

F = 
3
L 

z

L
m
F = N v 2x
L
So the pressure on the wall is:
Nm v 2
F
1
=
P=
3 AL
A
=
1 Nm v
3 V
2
Thermal Physics (30 of 45)
The Kinetic Theory of Gases
P=
Rewriting,
1 Nm v
3 V
(2
)
PV = 2 N 1 m v 2 = NkT
3
so
2
(
2 1 mv2
3 2
) = kT
( KE) = 12 m v 2 = 32 kT
The average translational kinetic energy of the molecules
in an ideal gas is directly proportional to the temperature
of the gas.
Thermal Physics (31 of 45)
The Kinetic Theory of Gases
Molecular Kinetic Energy
Temperature is a measure of the average
molecular kinetic energy.
mv2
2
3kT
KE =
2
m v 2 3kT
=
2
2
v (rms ) =
3kT
m
Thermal Physics (32 of 45)
Thermal Physics 10
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
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
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
The Kinetic Theory of Gases (Problem)
What is the total random kinetic energy of all the
molecules in one mole of hydrogen at a temperature
of 300 K.
Thermal Physics (36 of 45)
The Kinetic Theory of Gases (Problem)
Calculate the rms speed of a Nitrogen molecule (N2)
when the temperature is 100 oC.
Thermal Physics (37 of 45)
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 kinetic
energy of a gas molecule?
Thermal Physics (38 of 45)
Thermal Physics 10
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
The Kinetic Theory of Gases
Mean and rms Speed
6
Mean Speed:
3
1+ 6+ 4+ 2+ 6+ 3+ 2+ 5
=
8
2
6
1
2
v (mean ) = 3.6 m/s
5
4
rms Speed:
=
(1)2 + (6 )2 + (4 )2 + (2 )2 + (6 )2 + (3 )2 + (2 )2 + (5 )2
8
v (rms ) = 4.0 m/s
Thermal Physics (40 of 45)
Thermal Physics 10
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
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.
Thermal Physics (43 of 45)
Summary
Ideal gas law: PV = nRT
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:
( KE) = 12 m v 2 = 32 kT
Thermal Physics (44 of 45)