Statistical Physics

This classic text combines thermodynamics, statistical mechanics, and kinetic theory in a single unified presentation of thermal physics. The three-part treatment covers the principles of statistical thermodynamics, equilibrium statistics of special systems, and kinetic theory, transport coefficients, and fluctuations. Numerous problems with solutions. Supplemental reading. 1966 edition.

PART I Principles of statistical thermodynamics
1 The first law of thermodynamics
  1-1. Systems and state variables
  1-2. The equation of state
  1-3. "Large" and "small" systems; statistics of Gibbs versus Boltzman"
  1-4. "The First Law; heat, work, and energy"
  1-5. Precise formulation of the First Law for quasistatic change
  Problems
2 Elementary statistical methods in physics
  2-1. Probability distributions; binomial and Poisson distributions
  2-2. Distribution function for large numbers; Gaussian distribution
  2-3. Statistical dealing with averages in time; virial theorem
  Problems
3 Statistical counting in mechanics
  3-1. Statistical counting in classical mechanics; Liouville theorem and ergodic hypothesis
  3-2. Statistical counting in quantum mechanics
  Problems
4 The Gibbs-Boltzmann distribution law
  4-1. Derivation of the Gibbsian or canonical distribution
  4-2. Elucidation of the temperature concept
  4-3. The perfect gas; Maxwellian distribution
  4-4. Energy distribution for small and large samples; thermodynamic limit
  4-5. Equipartition theorem and dormant degrees of freedom
  Problems
5 Statistical justification of the Second Law
  5-1. Definition of entropy; entropy and probability
  5-2. "Proof of the Second Law for "clamped" systems"
  5-3. The Ehrenfest or adiabatic principle
  5-4. Extension of the Second Law to general systems
  5-5. Simple examples of entropy expressions
  5-6. Examples of entropy-increasing processes
  5-7. Third Law of thermodynamics
  Problems
6 Older ways to the Second Law
  6-1. Proof by the method of Carnot cycles
  6-2. Proof of Caratheodory
  Problems
7 Thermodynamic exploitation of the Second Law; mass transfer problems
  7-1. Legendre transformations and thermodynamic potentials
  7-2. Thermodynamics of bulk properties; extensive and intensive variables
  7-3. Equilibrium of two phases; equation of Clausius and Clapeyron
  7-4. "Equilibrium of multiphase, multicomponents systems; Gibbs' phase rule"
  7-5. Refined study of the two-phase equilibrium; vapor pressure of small drops
  Problems
8 The grand ensemble; classical statistics of independent particles
  8-1. Statistics of the grand ensemble
  8-2. Other modified statistics; Legendre-transformed partition functions
  8-3. Maxwell-Boltzmann particle statistics
  8-4. Particle versus system partition function; Gibbs paradox
  8-5. Grand ensemble formulas for Boltzmann particles
  Problems
9 Quantum statistics of independent particles
  9-1. Pauli exclusion principle
  9-2. Fermi-Dirac statistics
  9-3. Theory of the perfect Fermi gas
  9-4. Bose-Einstein statistics
  9-5. The perfect Bose gas; Einstein condensation
PART II Equilibrium statistics of special systems
10 Thermal properties of electromagnetic radiation
  10-1. Realization of equilibrium radiation; black body radiation
  10-2. Thermodynamics of black body radiation; laws of Stefan-Boltzmann and Wien
  10-3. Statistics of black body radiation; Planck's formula
  Problems
11 Statistics of the perfect molecular gas
  11-1. Decomposition of the degrees of freedom of a perfect molecular gas
  11-2. Center-of-mass motion of gaseous molecules
  11-3. Rotation of gaseous molecules
  11-4. The rotational heat capacity of hydrogen
  11-5. Vibrational motion of diatomic molecules
  11-6. The law of mass action in perfect molecular gases
  Problems
12 The problem of the imperfect gas
  12-1. Equation of state from the partition function
  12-2. Equation of state from the virial theorem
  12-3. Approximate results from the virial theorem; van der Waals' equation
  12-4. The Joule-Thomson effect
  12-5. Ursell-Mayer expansion of the partition function; diagram summation
  12.6 Mayer's cluster expansion theorem
  12-7. Mayer's formulation of the equation of state of imperfect gases
  12-8. Phase equilibrium between liquid and gas; critical phenomenon
  Problems
13 Thermal properties of crystals
  13-1. Relation between the vibration spectrum and the heat capacity of solids
  13-2. Vibrational bands of crystals; models in one dimension
  13-3. Vibrational bands of crystals; general theory
  13-4. Debye theory of the heat capacity of solids
  13-5. Vapor pressure of solids
  Problems
14 Statistics of conduction electrons in solids
  14-1. The distinction of metals and insulators in fermi statistics
  14-2. Semiconductors: electrons and holes
  14-3. Theory of thermionic emission
  14-4. Degeneracy and non-degeneracy: electronic heat capacity in metals
  14-5. "Doped" semiconductors: n-p junctions"
  Problems
15 Statistics of magnetism
  15-1. Paramagnetism of isolated atoms and ions
  15-2. Pauli paramagnetism
  15-3. Ferromagnetism; internal field model
  15-4. Ferromagnetism; Ising model
  15-5. Spin wave theory of magnetization
  Problems
16 Mathematical analysis of the Ising model
  16-1. Eigenvalue method for periodic nearest neighbor systems
  16-2. One-dimensional Ising model
  16-3. Solution of the two-dimensional Ising model by abstract algebra
  16-4. Analytic reduction of the results for the two dimensional Ising model
17 Theory of dilute solutions
  17-1. Thermodynamic functions for dilute solutions
  17-2. Osmotic pressure and other modifictions of solvent properties
  17-3. Behavior of solutes in dilute solutions; analogy to perfect gases
  17-4. Theory of strong electrolytes
  Problems
"PART III Kinetic theory, transport coefficients and fluctuations"
18 Kinetic justification of equilibrium statistics; Boltzmann transport equation
  18-1. Derivation of the Boltmann transport equation
  18-2. Equilibrium solutions of the Boltzmann transport equation; Maxwellian distribution
  18-3. Boltzmann's H-theorem
  18-4. Paradoxes associated with the Boltzmann transport equation; Kac ring model
  18-5. Relaxation rate spectrum for Maxwellian molecules
  18-6. Formal relaxtion theory of the Boltzmann equation
  Problems
19 Transport properties of gases
  19-1. Elementary theory of transport phenomena in gases
  19-2. Determination of transport coefficients from the Boltzmann equation
  19-3. Discussion of empirical viscosity data
  Problems
20 Kinetics of charge carriers in solics and liquids
  20-1. Kinetic theory of Ohmic conduction
  20-2. Nature of the charge carriers in matter; Nernst relation
  20-3. Nature of the electric carriers in metals; law of Wiedmann and Franz
  20-4. Separation of carrier density and carrier velocity; Hall effect
  Problems
21 Kinetics of charge carriers in gases
  21-1. Kinetics of the polarization force
  21-2. "High field" velocity distribution of ions and electrons in gases"
  21-3. Velocity distribution functions for electrons; formulas of Davydov and Druyvesteyn
22 Fluctuations and Brownian motion
  22-1. Equilibrium theory of fluctuations
  22-2. Brownian motion
  22-3. Spectral decompostion of Brownian motion ; Wiener-Khinchin theorem
  Problems
23 Connection between transport coefficients and equilibrium statistics
  23-1. Nyquist relation
  23-2. Kubo's equilbrium expression for electrical conductivity
  23-3. Reduction of the Kubo relation to those of Nernst and Nyquist
  23-4. Onsager relations
  Problem
Supplementary Literature
Answers to Problems
Index