Statistical Physics

Statistical Physics

by Gregory H. Wannier

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Overview

Statistical Physics by Gregory H. Wannier

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 This text, a forerunner in its field and now a classic, was the first to recognize the outdated reasons for their separation and to combine the essentials of the three subjects into one unified presentation of thermal physics.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.

Product Details

ISBN-13: 9780486654010
Publisher: Dover Publications
Publication date: 10/18/2010
Series: Dover Books on Physics
Edition description: Unabridged
Pages: 560
Product dimensions: 5.50(w) x 8.50(h) x (d)

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 solids 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

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