An Introduction to Statistical Thermodynamics

by Terrell L. Hill

Overview

"A large number of exercises of a broad range of difficulty make this book even more useful…a good addition to the literature on thermodynamics at the undergraduate level." — Philosophical Magazine
Although written on an introductory level, this wide-ranging text provides extensive coverage of topics of current interest in equilibrium statistical mechanics. Indeed, certain traditional topics are given somewhat condensed treatment to allow room for a survey of more recent advances.
The book is divided into four major sections. Part I deals with the principles of quantum statistical mechanics and includes discussions of energy levels, states and eigenfunctions, degeneracy and other topics. Part II examines systems composed of independent molecules or of other independent subsystems. Topics range from ideal monatomic gas and monatomic crystals to polyatomic gas and configuration of polymer molecules and rubber elasticity. An examination of systems of interacting molecules comprises the nine chapters in Part Ill, reviewing such subjects as lattice statistics, imperfect gases and dilute liquid solutions. Part IV covers quantum statistics and includes sections on Fermi-Dirac and Bose-Einstein statistics, photon gas and free-volume theories of quantum liquids.
Each chapter includes problems varying in difficulty — ranging from simple numerical exercises to small-scale "research" propositions. In addition, supplementary reading lists for each chapter invite students to pursue the subject at a more advanced level. Readers are assumed to have studied thermodynamics, calculus, elementary differential equations and elementary quantum mechanics.
Because of the flexibility of the chapter arrangements, this book especially lends itself to use in a one-or two-semester graduate course in chemistry, a one-semester senior or graduate course in physics or an introductory course in statistical mechanics.

Product Details

ISBN-13:	9780486652429
Publisher:	Dover Publications
Publication date:	01/01/1987
Series:	Dover Books on Physics
Edition description:	Revised ed.
Pages:	544
Product dimensions:	5.50(w) x 8.50(h) x (d)

Table of Contents

PART I. PRINCIPLES OF QUANTUM STATISTICAL MECHANICS
CHAPTER 1. STATISTICAL-MECHANICAL ENSEMBLES AND THERMODYNAMICS
1-1 Introduction
1-2 Ensembles and postulates
1-3 Canonical ensemble
1-4 Canonical ensemble and thermodynamics
1-5 Grand canonical ensemble
1-6 Micronomical ensemble
1-7 Other ensembles
CHAPTER 2. FURTHER DISCUSSION OF ENSEMBLES AND THERMODYNAMICS
2-1 Fluctuations
2-2 Thermodynamic equivalence of ensembles
2-3 Second law of thermodynamics
2-4 Third law of thermodynamics
PART II. SYSTEMS COMPOSED OF INDEPENDENT MOLECULES OR SUBSYSTEMS AND INDISTINGUISHABLE MOLECULES OR SUBSYSTEMS
CHAPTER 3. GENERAL RELATIONS FOR INDEPENDENT DISTINGUISHABLE AND INDISTINGUISHABLE MOLECULES OR SUBSYSTEMS
3-1 Independent and distinguishable molecules or subsystems
3-2 Independent and indistinguishable molecules or subsystems
3-3 Energy distribution among independent molecules
3-4 "Ensembles" of small, independent "systems"
CHAPTER 4. IDEAL MONATOMIC GAS
4-1 Energy levels and canonical ensemble partion function
4-2 Thermodynamic functions
4-3 Grand ensemble and others
4-4 Internal degrees of freedom
CHAPTER 5. MONATOMIC CRYSTALS
5-1 Einstien model of a monatomic crystal
5-2 General treatment of molecular vibrations in a monatomic crystal
5-3 The Debye approximation
5-4 Exact treatments of the frequency distribution problem
CHAPTER 6. CLASSICAL STATISTICAL MECHANICS
6-1 Introductory examples
6-2 More general systems
6-3 Phase space and ensembles in classical statistics
6-4 Maxwell-Boltzmann velocity distribution
"CHAPTER 7. INTRODUCTION TO LATTICE STATISTICS: ADSORPTION, BINDING, AND TITRATION PROBLEMS"
7-1 Ideal lattice gas (Langmiur adsorption theory)
7-2 Grand partition function for a single independent site or subsystem
7-3 Systems composed of independent and indistinguishable subsystems
7-4 Elasticity of and adsorption on a linear polymer chain
CHAPTER 8. IDEAL DIATOMIC GAS
8-1 Independence of degrees of freedom
8-2 Vibration
8-3 Rotation
8-4 Thermodynamic functions
CHAPTER 9. IDEAL POLYATOMIC GAS
9-1 Potential energy surface
9-2 Vibration
9-3 Rotation
9-4 Thermodynamic functions
9-5 Hindred internal rotation in ethane
9-6 Hindred translation on a surface
CHAPTER 10. CHEMICAL EQUILIBRIUM IN IDEAL GAS MIXTURES
10-1 General relations
10-2 Statistical derivation in a special case
10-3 Fluctuations in a simple chemical equilibrium
10-4 Examples of chemical equilibria
CHAPTER 11. THE RATE OF CHEMICAL REACTIONS IN IDEAL GAS MIXTURES
11-1 Potential surfaces
11-2 Absolute rate theory
11-3 A nonchemical application of the Eyring theory
CHAPTER 12. IDEAL GAS IN AN ELECTRIC FIELD
12-1 Thermodynamic background
12-2 Statistical-mechanical background
12-3 Dilute gas in an electric field
12-4 Lattice of noninteracting magnetic dipoles
CHAPTER 13. CONFIGURATION OF POLYMER MOLECULES AND RUBBER ELASTICITY
13-1 Freely jointed chain
13-2 Gaussian probability distribution for free polymer molecules
13-3 Rubber elasticity
PART III. SYSTEMS OF INTERACTING MOLECULES
CHAPTER 14. LATTICE STATISTICS
14-1 One-dimensional lattice gas (adsorption)
14-2 Elasticity of a linear polymer chain
14-3 Two-dimensional square lattice
14-4 Bragg-Williams approximation
14-5 Quasi-chemical approximation
14-6 First-order phase transitions
CHAPTER 15. IMPERFECT GASES
15-1 Virial expansion of a one-component gas
15-2 One-component classical monatomic gas
15-3 Two-component imperfect gas
15-4 Imperfect gas near a surface
15-5 Imperfect gas in an electric field
CHAPTER 16. APPROXIMATE CELL AND HOLE THEORIES OF THE LIQUID STATE
16-1 The van der Waals equation of state
16-2 Cell theories of liquids
16-3 Hole theories of liquids
16-4 Law of corresponding states
CHAPTER 17. DISTRIBUTION FUNCTIONS IN CLASSICAL MONATOMIC FLUIDS
17-1 Radial distribution function
17-2 Relation of thermodynamic functions to g( r )
17-3 Integral equation for g(r;x)
17-4 Formal definition of distribution functions
17-5 Surface tension
CHAPTER 18. DILUTE ELECTROLYTE SOLUTIONS AND PLASMAS
18-1 Debye-Hückel theory
18-2 Kirkwood theory of solutions
18-3 Electrolyte solutions
CHAPTER 19. DILUTE LIQUID SOLUTIONS
19-1 McMillan-Mayer solution theory
19-2 Applications of the McMillan-Mayer theory
19-3 Constant pressure solution theory
CHAPTER 20. THEORY OF CONCENTRATED SOLUTIONS
20-1 Lattice theory of solutions
20-2 Cell theories of binary solutions
20-3 "Random-mixing, corresponding-states theory "
20-4 Conformal solution theory
CHAPTER 21. POLYMER AND POLYELECTROLYTE SOLUTIONS AND GELS
21-1 Wall theory of rubber elasticity
21-2 Flory-Hugging polymer solution theory
21-3 Swelling of polymer gels
21-4 Swelling of polyelectrolyte gels
21-5 Isolated polymer or polyelectrolyte molecules in solution
21-6 Second Virial coefficient in polymer and polyelectrolyte solutions
CHAPTER 22. QUANTUM STATISTICS
22-1 Introduction to Fermi-Dirac and Bose-Einstein statistics
22-2 Ideal Fermi-Dirac gas; electrons in metals
22-3 Ideal Bose-Einstein gas; helium
22-4 Blackbody radiation (photon gas)
22-5 Quantum statistics with intermolecular interactions
22-6 The factors hn and N! in classical statistics
22-7 Free-volume theories of quantum liquids
22-8 Gas of symmetrical diatomic modules at low temperatures
APPENDIX I. Natural Constants
APPENDIX II. Maximum-Term Method
APPENDIX III. Method of Undetermined Multipliers
APPENDIX IV. The Lennard-Jones Potential
APPENDIX V. Normal Coordinate Analysis in a Special Case
APPENDIX VI. Vibrational Frequency Distribution in a Solid Continuum
APPENDIX VII. Generalized Coordinates
INDEX