1. ? Thermal Physics Thermodynamics kinetic theory statistical mechanics
Introductory remarks
Thermodynamics
Thermal Physics
kinetic theory
statistical mechanics ?
What is the scope of thermodynamics
macroscopic or large scale behavior of systems
involving concepts like:
- heat
Typical problems
- temperature
- entropy
heat
work

2. experimental experience
What
does
it mean ?
macroscopic or large scale systems
gas
liquid
solid
magnet
electromagnetic
radiation
Of remarkable universality
Thermodynamics: Theory based on a small number of principles
generalizations of
experimental experience

3. expansion coefficient quantities determined from experiments
Typical example of a thermodynamic relation :
expansion coefficient
quantities determined from
experiments
no microscopic theory
compressibility
But:
relation of very general validity independent of microscopic details of the system
Heat capacity at constant pressure/volume
(Definition of CP/V and meaning of the relation later in this course)
Calculation of the actual magnitude of
- heat capacity
expansion coefficient
compressibility
kinetic theory,
Statistical mechanics

4. Basic concepts Temperature people have a subjective perception
of temperature
Temperature
but
physical theory requires a precise
definition of temperature
Macroscopic bodies possess a temperature characterized by a number
-Temperature is a scalar quantity
-we can find out whether
temperature
of body B
temperature
of body A

5. =: thermal equilibrium
Equality of temperature
body A of
temperature
body B of
temperature
sufficient long waiting
no further change in measurable properties of A and B
=: thermal equilibrium
( is the empirical temperature in contrast with
the absolute thermodynamic temperature T)
Instead talking about bodies A and B let us introduce the concept of a
system

6. Thermodynamic System:
Certain portion of the universe with a
boundary
possibility to define what is part of the system and what is
surrounding
Moveable wall which
Surrounding
controls flux of
mechanical energy
real boundary
(imaginary boundaries can also be defined)
Here: gas enclosed by the boundary
no particle exchange with surrounding
Example of a closed system
open:
particle exchange possible

7. Zeroth law of thermodynamics:
When any two systems are each separately in thermal equilibrium
with a third, they are also in thermal equilibrium with each other.
foundation of temperature measurement
System 3
(e.g. thermometer)
System 1
System 2

8. Zeroth law and temperature measurement Thermometer:
System* with thermometric
property
parameter which
changes with
temperature
System 3
(length, pressure, resistance, …)
System 2
System 1
3 unchanged
1 and 3
come to equilibrium
2 and 3
in equilibrium
1 and 2
in equilibrium
temperature of 1= temperature of 2
Note: Thermometer requires no calibration to verify equality of temperatures
* “small” enough not to influence 1/2

9. ? X: X: X: How to assign a numerical value to the temperature
Common thermometers and corresponding thermometric property X
Liquid-in-glass thermometers X:
change of the level of the liquid with temperature
resistance thermometer X:
change of the resistance with temperature
thermocouple X:
change of the voltage with temperature

10. Defining temperature scales
Constant–volume gas thermometer X:
change of the pressure with temperature
h determines the gas pressure
in the bulb according to
Const. volume
achieved by raising
or lowering R
Mercury level on left side of the tube const.
Defining temperature scales
Ratio of temperatures =
Ratio of thermometric parameters
For all thermometers we set: 1

11. Assign a numerical value to a standard fixed point2
triple point of water

12. Assign arbitrary value
to the triple point
(in general)
(for the gas thermometer)
:  depends on the gas pressure and the type of filling gas (O2, Air, N2, H2)
or more generally speaking  depends on the chosen thermometer
However, experiments show:
 independent of the gas type and pressure for
empirical gas temperature
with 3= degrees
absolute or thermodynamic temperature
William Thomson Kelvin, 1st Baron
( )

13. assigning a numerical value to the triple point temperature 3
Before 1954 gas temperature defined by two fixed points 1
Steam point (normal boiling point of pure water)
ice point (melting point of ice at pressure of 1 atmosphere) 2
Defined:
degrees
with
experiment
Experiment shows:
Triple point temperature
is 0.01 degree above
3= degrees

14. Celsius and Fahrenheit scales
Click for Fahrenheit to Celsius converter
Temperature differences on the Kelvin and Celsius scale
are numerically equal
Ice temperature on Celsius scale 0.00oC
Anders Celsius
Fixed points again:
- steam point (2120F)
- ice point (320F)
Difference 180 degrees
instead of 100 degrees
Gabriel Daniel
Fahrenheit

15. State of a system equilibrium state T=Tice= 273K Remember:
Equilibrium (state) of a system
equilibrium state
Non-equilibrium
T=Tice= 273K
T=TL>273K
Steady state no time dependence

16. State of a system is determined by a set of state variables
Properties which specify
the state completely
In the equilibrium state the # of variables is kept to a minimum
Example: temperature T and volume V can specify the state of a gas in accordance
with the equation of state P=P(V,T)
independent variables
spanning the state space
(here: 2 variables span a 2-dim.state space)
Particular example of a PVT -systems
-Equation of state of an ideal gas

17. In the limit P->0 all gases obey the equation of state of an
Experiments show:
In the limit P->0 all gases obey the equation of state of an
ideal gas
Boyle's Law
Charles and Gay-Lussac's Law
animations from:

18. universal gas constant R=8.314 J/(mol K)
can also expressed as
R=NA kB
where NA= /mol: Avogadro’s #
Experiment: const.=n R
and kB= J/K
Boltzman constant
# of moles
Ideal gas equation of state or
N=nNA # of particles

19. + A general form treating P,V and T symmetrically for the ideal gas
State of a closed system in thermal equilibrium
is also characterized by the
internal energy U=U(T,V)
kinetic energy
(disordered motion)
internal energy U +
potential energy
(particle interaction)
-for an ideal gas one obtains U=U(T)
independent of the volume
(because no particle-particle interaction)

20. Variables describing the state of a system can be classified into
extensive
Scale with the size of the system 1
variables
-independent of system size
-can be locally measured
intensive 2
but
Example:
Volume extensive
temperature intensive
V3=2V0
V2=V0
V1=V0 + =
T1=T0
T3=T0
T2=T0 I II
III

21. = E E + = + U1=const. V0 U2=const. V0 U3=const. 2V0 Remark:
In conventional thermodynamics one usually assumes extensive behavior
of the internal energy for instance. I
U1=const. V0 II
U2=const. V0
III
U3=const. 2V0 + =
Non-extensive
thermodynamics
But this is not always the case
Consider the energy E of a homogenously charged sphere:
Click figure for research
Article on nonextensivity E
Compare
homework + E =

22. Heat T1
> T2
System 2
System 1
Heat Q flows from
1 to 2
Heat is an energy transferred from one system to another because of temperature difference
1/2
and not a state function
Heat is not part of the systems
Do not confuse heat with the internal energy of a system

23. Heat Q is measured with respect to the system
Sign Convention
Heat Q is measured with respect to the system
System
Q>0
Heat flow into the system
Q>0
System
Q<0
Heat flow out of the system

24. Heat Capacity and Specific Heat
T=T0
Transfer of small quantity of
heat Q
T=Tf
System reaches new equilibrium at T=Tf>T0
Temperature increase T=Tf-T0
Constant pressure heat capacity:
Constant volume heat capacity: 1 2 Q Q m
fixed position
V=const.
P=const.

25. CV (1+ 2)= CV (1) +CV(2 ) n M Heat capacities are extensive:
System 1
CV(1)
CV (1+ 2)=
CV (1) +CV(2 )
System 2
CV(2)
Extensive heat capacity
# of moles or the mass
specific heat
, e.g.: n M

26. CV( ) CV( ) < cvM( ) cVM( ) = however specific heat:
Material property independent of the sample size
CV( )
CV( )
<
however
cvM( )
cVM( ) =
specific heat:

27. Specific heat at constant volume
cvM
But:
specific heat
depends on material
1 kg
Temperature increase
Amount of heat
Specific heat at constant volume

28. 3R In general: Specific heat depends on the state of the system
Example: 3R
Classical limit
If thermal expansion of a system negligible and cV  const.
cP  const.
where