Table of Contents

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