1. Heat Q vs Work W and efficiency
Carnot cycle
reversible
Maximal efficiency
depends on
(TH -TC)
Transformation of heat
into work always
involves losses
(QC)
1824
Sadi Carnot ( )

2. Fundaments of thermodynamics
First law: conservation of energy U
Rudolf Clausius
Second law:
transformations
(processes)
1854
Äquivalenzwert
der Verwandlung
R. Clausius Philosophical Magazine, 12 (1856) p.81

3. Statistical thermodynamics: History
Daniel Bernouilli
Hydrodynamica (1738): Heat = kinetic (movement) energy

4. Statistical thermodynamics: History
James Maxwell
1859: Maxwell distribution of velocities in gases

5. Statistical thermodynamics: History
Maxwell-Boltzmann distribution
Boltzmann Transport Equation (BTE)
Number of molecules with velocity v
Ludwig Boltzmann
1896: Lectures on gas theory

6. Statistical thermodynamic Entropy
1877: Boltzmann entropy
S measure for “statistical mixedupness”
Ω number of micro states of a
system in equilibrium as a macro state
Ludwig Boltzmann

7. Statistical thermodynamic Entropy
Ω number of micro states of a
system in equilibrium as a macro state
Ludwig Boltzmann

8. Statistical thermodynamic Entropy
Ω number of micro states of a
system in equilibrium as a macro state
Max Planck
Boltzmann constant

9. Statistical thermodynamic Entropy
S increases with temperature
Ludwig Boltzmann

10. Statistical thermodynamic Entropy
Ludwig Boltzmann

11. Modern classical thermodynamics
Third law (Nernst)
Hermann Walther Nernst

12. Statistical thermodynamics: History
Boltzmann distribution
Average number of molecules with energy εi
Erwin Schrödinger
Quantum mechanics: discrete energy states εi

13. Statistical thermodynamics: History
Boltzmann distribution
Chance of molecule to have energy εi
Entropy of the system
Erwin Schrödinger

15. Statistical thermodynamics: History
Boltzmann Transport Equation (BTE)
Ludwig Boltzmann
1896: Lectures on gas theory

16. Statistical thermodynamic Entropy
Zentralfriedhof
Vienna
Ludwig Boltzmann

18. Statistical Thermodynamics : Boltzmann distribution
Two level system

19. Statistical Thermodynamics: Boltzmann distribution

21. Entropy change for changing volume
Reversible, isothermal, isochoric “compression”
Rev., isothermal, isobaric expansion
Irreversible, isothermal expansion

22. Boltzmann distribution for changing volumeX

23. Boltzmann entropy for changing volumeX
low q
q is a measure for the number
of thermally accessible states
high q

24. Two ways to change Boltzmann entropy
W: #micro-states
Perfect atomic gas:
Perfect atomic gas:

25. Two ways to increase Boltzmann entropy
(for 4 constant CV values)

26. Temperature dependence of the entropy

27. @ all T [Cl2(g)]
@ 298 K
Atkins: Table 2C.5 (T = 298 K)
@ all T [Cu(s)]
@ 298 K

28. @ 298 K
@298 K
Atkins: Table 2C.5 (T = 298 K)
@298 K

30. Statistical Thermodynamics: First law
random (thermal) motion
ordered motion

31. Statistical Thermodynamics: Second law
spontaneous process:
energy dispersion
ordered  disordered motion
non-spontaneous process:
needs work
disordered  ordered motion

32. Stat. Thermo: reaction equilibria: T-dependence of K
endothermic
exothermic

33. Stat. Thermo: reaction equilibria: Density of states ρ

34. Stat. Thermo: reaction equilibria: Density of states ρ

36. Stat. Thermo: reaction equilibria: P-dependence of K
Classical Thermodynamics: 1 2
Inert gas

37. Stat. Thermo: reaction equilibria: P-dependence of K
Statistical Thermodynamics:
Boltzmann Distr. 1 2
Inert gas

39. Stat. Thermo: reaction equilibria: P-dependence of K2 1
Dissociation equilibrium
Classical Thermodynamics:
(Perfect gases)

40. Stat. Thermo: reaction equilibria: P-dependence of K2 1

41. Stat. Thermo: reaction equilibria: P-dependence of K
Statistical Thermodynamics: 2A V2 V1 A2 1 2

42. ? Stat. Thermo: reaction equilibria: P-dependence of KV2 V1 1 2
Boltzmann Distr. ?
Too complicated
Elective Stat. Thermod.