Statistical Physics: (Dover Books on Physics)

Until recently, the field of statistical physics was traditionally taught as three separate subjects: thermodynamics, statistical mechanics, and kinetic theory. This text, a forerunner in its field and now a classic, was the first to recognise the outdated reasons for their separation and to combine the essentials of the three subjects into one unified presentation of thermal physics. It has been widely adopted in graduate and advanced undergraduate courses, and is recommended throughout the field as an indispensable aid to the independent study and research of statistical physics.Designed for a one-year course of instruction for non-specialist graduate students, or advanced undergraduates, the book is divided into three parts. Principles of Statistical Thermodynamics (Part I) covers the first and second laws of thermodynamics, elementary statistical methods in physics, and other topics, including an especially clear and enlightening discussion of thermodynamic potentials and their applications. Part II, devoted to equilibrium statistics of special systems, offers excellent coverage of the imperfect gas, lattice dynamics, the statistics of semiconductors, the two-dimension Ising model, and a particularly lucid chapter on dilute solutions. Moreover, the treatment of topics in solid state physics is more extensive than is usually found in books on statistical mechanics. Kinetic theory, transport coefficients, and fluctuations comprise Part III, with a fine presentation of the Kac ring model; the Boltzmann transport equation; kinetics of charge carriers in solids, liquids, and gases; fluctuations and Brownian motion, and more. A liberal quantity of problems has been added to each chapter, including a special section of ""recommended problems,"" whose solutions will insure an adequate understanding of the text. Solutions of all problems will be found at the back of the book along with a list of supplementary literature.

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