Thermodynamics and Statistical Mechanics: An intermediate level course

Why study thermodynamics?......Page 5
Thermodynamics......Page 6
The need for a statistical approach......Page 7
Microscopic and macroscopic systems......Page 9
Thermodynamics and statistical thermodynamics......Page 10
Classical and quantum approaches......Page 11
What is probability?......Page 12
Combining probabilities......Page 13
The two-state system......Page 15
Combinatorial analysis......Page 16
The binomial distribution......Page 18
The mean, variance, and standard deviation......Page 19
Application to the binomial distribution......Page 21
The Gaussian distribution......Page 24
The central limit theorem......Page 29
Specification of the state of a many particle system......Page 31
The principle of equal a priori probabilities......Page 33
The H theorem......Page 36
The relaxation time......Page 41
Reversibility and irreversibility......Page 42
Probability calculations......Page 43
Behaviour of the density of states......Page 44
A brief history of heat and work......Page 47
Macrostates and microstates......Page 49
The microscopic interpretation of heat and work......Page 50
Quasi-static processes......Page 52
Exact and inexact differentials......Page 54
Thermal interaction between macrosystems......Page 60
Temperature......Page 64
Mechanical interaction between macrosystems......Page 68
General interaction between macrosystems......Page 70
Entropy......Page 73
Properties of entropy......Page 80
Uses of entropy......Page 82
Entropy and quantum mechanics......Page 85
The laws of thermodynamics......Page 89
Introduction......Page 90
The equation of state of an ideal gas......Page 91
Heat capacity or specific heat......Page 95
Calculation of specific heats......Page 98
Isothermal and adiabatic expansion......Page 99
Hydrostatic equilibrium of the atmosphere......Page 101
The isothermal atmosphere......Page 102
The adiabatic atmosphere......Page 104
Heat engines......Page 108
Refrigerators......Page 117
Boltzmann distributions......Page 119
Paramagnetism......Page 123
Mean values......Page 127
Partition functions......Page 130
Ideal monatomic gases......Page 132
Gibb's paradox......Page 135
The equipartition theorem......Page 138
Harmonic oscillators......Page 141
Specific heats......Page 143
Specific heats of gases......Page 146
Specific heats of solids......Page 152
The Maxwell distribution......Page 162
Symmetry requirements in quantum mechanics......Page 169
An illustrative example......Page 172
Formulation of the statistical problem......Page 174
Fermi-Dirac statistics......Page 175
Photon statistics......Page 178
Bose-Einstein statistics......Page 179
Maxwell-Boltzmann statistics......Page 180
Quantum statistics in the classical limit......Page 181
The Planck radiation law......Page 184
Black-body radiation......Page 188
The Stefan-Boltzmann law......Page 190
Conduction electrons in a metal......Page 192
White-dwarf stars......Page 198
The Chandrasekhar limit......Page 201
Neutron stars......Page 203