1. Chapter 10: Thermal Physics
Temperature and the Zeroth Law of
Thermodynamics
Terminology
Two objects are in thermal contact if energy can be exchanged
between them.
Two objects are in thermal equilibrium if they are in thermal contact
and there is no net exchange of energy.
The exchange of energy between two objects because of differences
in their temperature is called heat. But what is temperature!
Zeroth law of thermodynamics
If objects A and B are separately in thermal equilibrium with a third
object C, then A and B are in thermal equilibrium with each other.
Two objects in thermal equilibrium with each other are at the same
temperature.

2. Thermometers and Temperature Scales
Thermometers are devices used to measure the temperature of
an object or a system.
When a thermometer is in thermal contact with a system, energy is
exchanged until the thermometer and the system are in thermal
equilibrium with each other.
All the thermometers use some physical properties that depend on
the temperature. Some of these properties are:
1) the volume of a fluid
2) the length of a solid
3) the pressure of a gas held at constant volume
4) the volume of a gas held at constant pressure
5) electric resistance of a conductor
6) the color of very hot object.

3. Thermometers and Temperature Scales
Thermometer (cont’d)
One common thermometer consists of a mass of liquid: mercury or
alcohol. The fluid expands into a glass capillary tube when its
temperature rises.
0oC (Celsius) 100oC
When the cross-sectional area of the tube
is constant, the change in volume of the
liquid varies linearly with its length along
the tube.
The thermometer can be calibrated by
placing it in thermal contact with
environments that remain at constant temp.
Two of such environments are:
1) a mixture of water and ice in thermal
equilibrium at atmospheric pressure.
2) a mixture of water and steam in thermal
Freezing
point
Boiling
point

4. Thermometers and Temperature Scales
Constant-volume gas thermometer and the Kelvin scale
A constant-volume gas thermometer measures the pressure of
the gas contained in the flask immersed in the bath. The volume
of the gas in the flask is kept
constant by raising or lowering
reservoir B to keep the mercury
level constant in reservoir A.

5. Thermometers and Temperature Scales
Constant-volume gas thermometer and the Kelvin scale
It has been experimentally
observed that the pressure varies
linearly with temperature of
a fixed volume of gas, which does
not depend on what gas is used.
It has been experimentally
observed that these straight lines
merge at a single point at temp.
oC at pressure = 0.
This temperature is called absolute
zero, which is the base of the Kelvin temperature scale T=TC
measured in kelvin (K) where TC is temperature in Celsius..
0 K = oC

6. Thermometers and Temperature Scales
The common temperature scale in US is
Fahrenheit:

7. Thermal Expansion of Solids and Liquids
Thermal (linear) expansion
Thermal expansion : As temperature of a substance increases,
its volume in general increases. This phenomenon is called
thermal expansion.
The overall thermal expansion of an object is a consequence of the
change in the average separation between its constituent atoms or
molecules.
If the thermal expansion of an object is sufficiently small compared
with the object’s initial dimensions, the change in any dimension is,
to a good approximation, proportional to the first power of the temp.
change.
L0 is the initial length, L is the final length, and a is called
the coefficient of linear expansion for a given material (unit: ( oC) -1 ).

8. Thermal Expansion of Solids and Liquids
Thermal area expansion
Because the linear dimensions of an object change due to variations
in temperature, it follows that the surface area and volume of the
object also change.
Consider a square of material having an initial length L0 on a side
and therefore initial area A0=L02. As the temperature increases, the
length of each side increase to:
The new area is then:
g=2a : coefficient of area expansion

9. Thermal Expansion of Solids and Liquids
Thermal volume expansion
In a similar fashion we can show that the increase in volume of
an object accompanying a change in temperature is:
b : coefficient of area expansion
Note that b=3a if the
coefficient of linear
expansion of the object
is the same in all
directions.

10. Thermal Expansion of Solids and Liquids
Examples
Some applications of thermal expansion
Thermal expansion joint
A extreme hot day

11. Thermal Expansion of Solids and Liquids
Examples (cont’d)
Bimetal

12. Thermal Expansion of Solids and Liquids
Examples (cont’d)
Example 10.3 : Expansion of a railroad track
A steal rail road has a length of m when the temperature
is 0oC. What is the length on a hot day when the temperature is
40.0oC?
Find the stress if the track cannot expand.

13. Thermal Expansion of Solids and Liquids
Examples (cont’d)
Example 10.4 : Rings and rods
A circular copper ring at 20.0oC has a hole with an area of 9.98 cm2.
What minimum temperature must it have so that it can be slipped
onto a steel metal rod having a cross-sectional area of 10.0 cm2?
(b) If the ring and the rod are heated simultaneously, what change in
temperature of both will allow the ring to be slipped onto the end
of the rod?

14. Thermal Expansion of Solids and Liquids
Examples (cont’d)
Example 10.5 : Global warming and coastal flooding
Estimate the fractional change in the volume of Earth’s oceans due
to an average temperature change of 1oC?
(b) Use the fact that the average depth of the ocean is 4.00x103 m to
estimate the change in depth. bwater =2.07x10-4 (oC)-1.

15. Macroscopic Description of an Ideal Gas
An ideal gas is a collection of atoms or molecules that move
randomly and exert no long-range forces on each other. Each
particle of the ideal gas is individually point-like, occupying a
negligible volume.
Low-density/low-pressure gases behave like ideal gases.
Most gases at room temperature and atmospheric pressure
can be approximately treated as ideal gases.
Equation of state
The pressure P, volume V, temperature T and amount n of gas
in a container are related to each other by an equation of state.
In general, equation of state is complex but for an ideal gas it
is simple.

16. Macroscopic Description of an Ideal Gas
Avogadro’s number
The same number of particles is found in a mole of a substance.
This number is called Avogadro’s number NA=6.02x1023 particles/mole.
The mass in grams of one Avogadro’s number of an element is
numerically the same as the mass of one atom of the element,
expressed in atomic mass u.
Atomic mass of hydrogen 1H is 1 u, and that of carbon 12C is 12 u.
12 g of 12C consists of exactly NA atoms of 12C. The molecular mass
of molecular hydrogen H2 is 2u, and NA molecules are in 2 g of H2 gas.
Molar mass of a substance
The molar mass of a substance is defined as the mass of one mole
of that substance, usually expressed in grams per mole.
Number of moles
The number of moles of a substances n is:
m : mass of the substance

17. Macroscopic Description of an Ideal Gas
Definition of a mole
One mole (mol) of any substance is that amount of the substance
that contains as many particles (atoms, or other particles) as there
are atoms in 12 g of the isotope carbon-12 12C.
One atomic mass unit is equal to 1.66x10-24 g.
The mass m of an Avogadro’s number of carbon-12 atoms is :
The mass per atom for a given element is:
1.66x10-24=1/6.02x1023

18. Macroscopic Description of an Ideal Gas
Ideal gas law (Equation of state for ideal gas)
Boyle’s law
When a gas is kept at a constant temperature, its pressure is
inversely proportional to its volume.
Charles’s law
When the pressure of a gas is kept constant, its volume is
directly proportional to the temperature.
Gay-Lussac’s law
When the volume of a gas is kept constant, its pressure is
directly proportional to the temperature.
P : pressure, V : volume, T : temperature in K
R : universal gas constant 8.31 J/(mole K)
L atm/(mol K)
1 L (litre) = 103 cm3 = 10-3 m3
Ideal gas law:
The volume occupied by 1 mol of an ideal gas at atmospheric
pressure and at 0oC is 22.4 L

19. Macroscopic Description of an Ideal Gas
Ideal gas law (Equation of state for ideal gas) (cont’d)
P : pressure, V : volume, T : temperature in K
R : universal gas constant 8.31 J/(mole K)
L atm/(mol K)
1 L (litre) = 103 cm3 = 10-3 m3
Ideal gas law:
The volume occupied by 1 mol of an ideal gas at atmospheric
pressure and at 0oC is 22.4 L
Defining kB=R/NA=1.38x10-23 J/K (Boltzmann’s constant),

20. Macroscopic Description of an Ideal Gas
Examples
Example 10.7 : Message in a bottle
A corked bottle was found with a message in air inside at atmospheric
pressure and at T=30.0oC. The cork has a cross-sectional area of 2.30
cm2. The finder placed the bottle over a fire to eject the cork, which
happened at T=99oC. (a) What was the pressure just before the cork
popped out from the bottle?
(b) What force of friction held the cork in place? Neglect any change in
in volume of the bottle.

21. Macroscopic Description of an Ideal Gas
Examples
Example 10.8 : Submerging a balloon
A balloon with volume m3 is attached to 2.50x102 kg iron weight
and tossed overboard into a freshwater. The air in the balloon initially
at atmospheric pressure. The system fails to sink and there are no
more weights, so a skin diver decides to drag it deep enough so that
the balloon will remain submerged. Ignore the weight of the balloon
material. (a) Find the volume of the balloon at the point where the
system will remain submerged in equilibrium?
Solve for Vbal.

22. Macroscopic Description of an Ideal Gas
Examples
Example 10.8 : Submerging a balloon (cont’d)
(b) What is the balloon’s pressure at that point?
Vi=0.500 m3
Vf=0.219 m3
(c) To what minimum depth must the balloon be dragged?

23. Macroscopic Description of an Ideal Gas
Kinetic theory of gases
Assumptions
The number of molecules in the gas is large, and the average
separation between them is large compared with their dimension.
A large number of molecules behave statistically in a stable fashion.
Large separation between molecules allows us to neglect the
volume occupied by a molecule.
The molecules obey Newton’s laws of motion, but as a whole they
move randomly.
Randomness guarantees that any molecule move in any direction
with equal probability. From this randomness emerges “regularity”.
The molecules interact only through short-range forces during
elastic collisions.
Lack of long-range force is consistent with the ideal gas model.
The molecules make elastic collisions with the walls.
All molecules in the gas are identical.

24. Macroscopic Description of an Ideal Gas
Kinetic theory of gases
Molecular model for the pressure of an
ideal gas
Consider the collision of a molecule moving
with a velocity –vx in x-direction toward the
left hand wall. After colliding elastically, the
molecule moves in the x-direction with a
velocity vx. The change in momentum is:
The magnitude of the average force exerted
by a molecule on the wall in time Dt is:
The time interval Dt between two collisions
with the same wall is :

25. Macroscopic Description of an Ideal Gas
Kinetic theory of gases
Molecular model for the pressure of an ideal gas (cont’d)
The force imparted to the wall in a time Dt by a single molecule is:
The total force exerted by all the molecules on the wall is then:
randomness
average translational
kinetic energy

26. Macroscopic Description of an Ideal Gas
Kinetic theory of gases
Molecular interpretation of temperature
Ideal gas law + pressure in terms of average kinetic energy :
The temperature of a gas is a direct measure of
the average molecular kinetic energy of the gas.
The average translational kinetic energy per molecule
is (3/2) of kBT.
The total translational kinetic energy
of N molecules of gas

27. Macroscopic Description of an Ideal Gas
Kinetic theory of gases
Internal energy, root-mean-square speed
For a monatomic gas, the translational kinetic energy is the only
type of energy that molecules can have. Therefore the internal energy
U of a monatomic gas is :
For diatomic and polyatomic molecules, additional types of energy
sources are available from the vibration and rotation of molecules.
The square root of is called the root-mean-square (rms) speed of
molecules.
O2 : M =32x10-2 kg/mol
vrms =1.0x103 m/s