Thermodynamics

1. Thermodynamics
SOME DEFINITIONS:
• THERMO – related to heat
• DYNAMICS – the study of motion
• SYSTEM – an object or set of objects
• ENVIRONMENT – the rest of the universe
• MICROSCOPIC – at an atomic or molecular level
• MACROSCOPIC – at a level detectable by our senses
THERMODYNAMICS
 is the study of the relationship between heat and motion.
 is a macroscopic description of the properties of a system
using state variables (e.g. volume, temperature, pressure)
Atoms are in constant motion, which increases with temperature.

2. The Phases of Matter
Solid Liquid Gas or Vapor
+ - + - + - - +
- + - + - + - + -
- - + - + - + + -
- - + - + - + + -
- - + - + - + + -
- - + - + - + + -
- - + - + + + -
+ - + - + - + + -
- - + - + - + -
- - + - + - + + -
+ - + - + - + -
Plasma
Increasing Temperature
Solids and liquids composed of atoms joined together at distances
of about 10-10 m by attractive electrical forces. In gases, vapors
and plasmas, the atoms, molecules or ions are in random motion.

3. Temperature
Temperature
• is a measure of how hot or cold an object is.
• is measured by a thermometer.
Thermometers are based on physical properties of
objects that change with temperature, for example:
 volume of a liquid
 length of a solid
 pressure of a gas
 electrical resistance of a solid
 electrical potential difference between two solids.

4. Common Temperature Scales
Fahrenheit:
• Based on the ability of farm animals to survive for
extended periods without attention.
• (0 ºF is the coldest and 100 ºF is the hottest).
Celsius or Centigrade:
• Based on the physical properties of water on the
earth’s surface at sea level (0 ºC is the freezing point
and 100 ºC is the boiling point).
T(ºC) = (5/9)[T(ºF) – 32]
T (ºF) = (9/5)T(ºC) + 32

5. Absolute (Kelvin) Temperature Scale
The volume occupied by any gas at constant pressure is an
increasing linear function of temperature, that always
extrapolates to zero at –273.15 ºC (called absolute zero).
This is called
Charles’s Law
and is the basis
for the absolute
or Kelvin (K)
temperature
scale.
T(K) = T(ºC) + 273.15

6. Absolute or Kelvin Temperature Scale
 The absolute or Kelvin scale is the true physical
temperature scale.
 T = -273.15 ºC = 0 K is the lowest temperature that
can be defined for any physical system.
 Absolute zero of temperature (0 K) is a theoretical
limit that can never be reached in a physical system.
 Experiments on Bose-Einstein Condensation in gases have
reached the nano-Kelvin (10-9 K) range (1998, 2001 Nobel
Prizes in physics)!
 The degree steps in the Celsius and Kelvin scales
are chosen to be the same: ΔT(ºC) = ΔT(K).

7. Zero’th Law of Thermodynamics
Our experience tells us that objects placed in contact
will eventually reach the same temperature. We say
that they are then in thermal equilibrium. This is the
basis for
The Zero’th Law of Thermodynamics:
If two objects A and B are in thermal equilibrium
with a third object C, then A and B are in thermal
equilibrium with each other.
Objects or systems in thermal equilibrium have the
same temperature. This is the physical basis for the
definition of temperature.

8. Review Questions
• Can objects that have different
temperatures be in thermal equilibrium
with each other?
• Is it possible for two objects to be in
thermal equilibrium if they are not
touching each other?

9. Thermal Expansion
Most materials expand when heated:
 The average distance between atoms increases as the
temperature is raised.
 The increase is proportional to the change in
temperature (over a small range).
Consider an object of length Li at temperature Ti
 If the object is heated or cooled to temperature Tf
Lf – Li = α Li (Tf – Ti) or ΔL = α Li ΔT
α = coefficient of linear expansion [ºC-1]
(α is a property of the material)

10. Thermal Expansion of Solids and Liquids
For the same
temperature change,
the thermal expansion
of liquids is greater than
that of solids.
Linear Expansion:
ΔL = α Li ΔT
Area Expansion:
ΔA = 2α Ai ΔT
Volume Expansion
ΔV = 3α Vi ΔT
Material α (ºC-1)
Invar 0.9 x 10-6
Glass 9 x 10-6
Concrete 12 x 10-6
Copper 17 x 10-6
Lead 29 x 10-6
Mercury 61 x 10-6
Gasoline 320 x 10-6

11. Example: Thermal Expansion
A concrete highway is built of slabs
12 m long at 20 ºC. How wide
should the expansion cracks
between the slabs be at 20 ºC to
prevent buckling if the range of
temperature is –30 ºC to +50 ºC ?
[The coefficient of linear expansion
of concrete is 12 x 10-6 ºC-1]

12. Liquid water has an unusual property.
• Water contracts when
heated from 0ºC to 4ºC,
then expands when
heated from 4 ºC to
100 ºC.
• Just above the freezing
point, the coldest (and
least dense) water rises
to the surface, and
lakes freeze from the
surface downward.
• This unusual property
permits aquatic life on
earth to survive winter!
Density of Water
0.95
0.96
0.97
0.98
0.99
1
0 4 12 20 50 100
Temperature in Celsius
g/(cm**3)

13. Thermal Stress
• Heat can stress materials if no allowance is
made for thermal expansion:
T
E
A
F
T
L
L
A
F
E
T
L
L
L
A
F
E
L












0
0
0
0
1
1
E = Young’s Modulus
Thermal Expansion
Thermal Stress

14. Molecular Model of an Ideal Gas
• The number of molecules is large.
• The average separation between molecules
is large compared to their dimensions.
• The molecules obey Newton’s laws of motion
and move randomly.
• The molecules collide elastically with each
other and with the container walls.
• The forces between molecules are negligible
except during collisions.
• All the molecules of the gas are identical.

15. Ideal Gas
 The relationship between the state variables,
pressure P, volume V and temperature T of a
system is called its equation of state.
 An ideal gas is one whose equation of state
is simple:
PV = nRT
n = number of moles (mole = 6.023 x 1023 molecules)
R = universal gas constant = 8.31 J/(mole K)
 Most gases near room temperature and
atmospheric pressure behave as ideal gases.

16. Avogradro’s Number and Molar Mass
• NA = 6.023 x 1023 = Avogadro’s number
• 1 mole is the quantity of any substance that
contains Avogadro’s number of atoms or
molecules.
• The gram-molecular-weight M of a substance is
the mass of one mole (molar mass) of that
substance:
 Helium (He) M = 4 g/mole
 Nitrogen (N2) M = 28 g/mole
 Oxygen (O2) M = 32 g/mole
 Methane (CH4) M = 16 g/mole

17. Equation of State of an Ideal Gas
• For a gas containing N atoms or molecules, the
number of moles n = N/NA.
• The ideal gas law:
PV = nRT = (N/NA)RT = N(R/NA)T = NkBT
where
kB = R/NA = 1.38 x 10-23 J/K (Boltzmann’s constant)
• The ideal gas law may be expressed:
PV = NkBT (N = number of atoms or molecules)
or
PV = nRT (n = number of moles)

18. Applying the Ideal Gas Law
For a ideal gas:
INITIAL STATE (1) FINAL STATE (2)
P1, V1, T1, n1 P2, V2, T2, n2
P1V1 = n1RT1 P2V2 = n2RT2
R = P1V1/(n1T1) R = P2V2/(n2T2)
2
2
2
2
1
1
1
1
T
n
V
P
T
n
V
P

2
2
2
1
1
1
T
V
P
T
V
P

or if n1 = n2
closed container
general case

19. Example Problem
If 18.75 mol of helium gas is at 10.0ºC and a
gauge pressure of 0.350 atm., calculate
a) The volume of the helium gas under these
conditions.
b) The temperature if the gas is compressed to
precisely half the volume at a gauge
pressure of 1.00 atm.

20. Review Questions
• When a cool mercury or alcohol
thermometer is inserted into boiling water,
it will initially indicate a lower
temperature before the reading starts to
increase. Explain.
• Will a grandfather clock that has been
calibrated at normal room temperature run
fast, slow or the same on a very hot day?

21. Review Questions
• An ideal gas in a sealed bottle at temperature T
occupies a volume V, and exerts a pressure P on the
walls of the bottle. What will happen to the
pressure if the temperature is doubled?
• Instead of a sealed container, the gas is contained in
a test tube with a movable piston on one end. The
temperature is then halved. What will happen to
a) the pressure?
b) the volume?

22. Heat
• Heat is defined as the energy that is transferred from one
system to another because of a difference in
temperature.
Units for Heat:
• calorie is the heat needed to raise the temperature of 1 g
of water by 1°C
• British thermal unit (Btu) is the heat needed to raise the
temperature of water weighing 1 lb by 1°F
1 cal = 4.186 J 1 kcal = 4186 J = 1 food Calorie
1 Btu = 1055 J = 252 cal
Heat = Q = Energy Transferred

23. • The internal energy U of a system is the total
energy of all the molecules in the system when
viewed from a reference frame that is at rest with
respect to the center of mass of the system.
• The internal energy includes the internal potential
energy within and between the molecules as well
as the kinetic energy of:
- random translational motion
- vibrational motion
- rotational motion.
Internal Energy of a System

24. Specific Heat
• The temperature change ΔT of an object due
to the transfer of an amount of heat Q
depends on:
– the mass of the object.
– the material of the object.
T
c
m
Q 

quantity of heat transferred
mass of the object
specific heat of the material
temperature change

25. Specific Heats of Some Materials at 20°C
Substance C [J/(kg °C)]
Water: liquid 4186
Water: ice 2100
Water: steam 2010
Ethyl Alcohol 2400
Wood 1700
Aluminum 900
Marble 860
Glass 840
Iron 450
Copper 390
Silver 230

26. Heat Capacity of Liquid Water
• Liquid water has the largest heat capacity of
almost any common substance (by a factor of
2 or more).
• Relatively large quantities of heat are
required to change the temperature of liquid
water.
• Bodies of water serve as an effective thermal
reservoirs.
• This property is responsible for moderate
climates near large bodies of water (e.g.
Pacific coast of the U.S., Europe).

27. Example Problem: Specific Heat
• How much heat is required to bring 0.3
liters of water in a glass cup (mass =
100 g) from room temperature (22°C) to
the boiling point?

28. Calorimetry
• Calorimetry is the measurement and
inventory of the heat in an isolated system
and application of conservation of energy.
• When different parts of an isolated system
are at different temperatures, heat will flow
from the part at higher temperature to the part
at lower temperature, if they are in contact.
Heat lost by one
part of system
Heat gained by another
part of system
=

29. Example Problem: Calorimetry
What will be the equilibrium temperature
when a 245-g block of copper at 300 ºC is
placed in a 150-g aluminum calorimeter cup
containing 820 g of water at 12.0 ºC?
Specific Heats:
cwater = 4186 J/(kg ºC )
caluminum = 900 J/(kg ºC )
ccopper = 390 J/(kg ºC )