An Introduction to Statistical Thermodynamics

An Introduction to Statistical Thermodynamics

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"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. "show more

Product details

  • Paperback | 544 pages
  • 137.16 x 213.36 x 30.48mm | 544.31g
  • Dover Publications Inc.
  • New York, United States
  • English
  • New edition
  • New edition
  • 106d.
  • 0486652424
  • 9780486652429
  • 216,575

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 INDEXshow more

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