Introductory Statistical Mechanics

Paperback | October 21, 1999

byRoger Bowley, Mariana Sanchez

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This book explains the ideas and techniques of statistical mechanics-the theory of condensed matter-in a simple and progressive way. The text starts with the laws of thermodynamics and simple ideas of quantum mechanics. The conceptual ideas underlying the subject are explained carefully; themathematical ideas are developed in parallel to give a coherent overall view. The text is illustrated with examples not just from solid state physics, but also from recent theories of radiation from black holes and recent data on the background radiation from the Cosmic background explorer. In thissecond edition, slightly more advanced material on statistical mechanics is introduced, material which students should meet in an undergraduate course. As a result the new edition contains three more chapters on phase transitions at an appropriate level for an undergraduate student. There are plentyof problems at the end of each chapter, and brief model answers are provided for odd-numbered problems. From reviews of the first edition: '...Introductory Statistical Mechanics is clear and crisp and takes advantage of the best parts of the many approaches to the subject' Physics Today

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This book explains the ideas and techniques of statistical mechanics-the theory of condensed matter-in a simple and progressive way. The text starts with the laws of thermodynamics and simple ideas of quantum mechanics. The conceptual ideas underlying the subject are explained carefully; themathematical ideas are developed in parallel ...

Roger Bowley is at University of Nottingham.
Format:PaperbackDimensions:368 pages, 9.45 × 6.61 × 0.79 inPublished:October 21, 1999Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198505760

ISBN - 13:9780198505761

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Table of Contents

1. The first law of thermodynamics1.1. Fundamental definitions1.2. Thermometers1.3. Different aspects of equilibrium1.4. Functions of state1.5. Internal energy1.6. Reversible changes1.7. Enthalpy1.8. Heat capacities1.9. Reversible adiabatic changes in an ideal gas1.10. Problems2. Entropy and the second law of thermodynamics2.1. A first look at the entropy2.2. The second law of thermodynamics2.3. The Carnot cycle2.4. The equivalence of the absolute and the perfect gas scale of temperature2.5. Definition of entropy2.6. Measuring the entropy2.7. The law of increase of entropy2.8. Calculations of the increase in the entropy in irreversible processes2.9. The approach to equilibrium2.10. Questions left unanswered2.11. Problems3. Probability and statistics3.1. Ideas about probability3.2. Classical probability3.3. Statistical probability3.4. The axioms of probability theory3.5. Independent events3.6. Counting the number of events3.7. Statistics and distribution3.8. Problems4. The ideas of statistical mechanics4.1. Introduction4.2. Definition of the quantum state of the system4.3. A simple model of spins on lattice sites4.4. Equations of state4.5. The second law of thermodynamics4.6. Logical positivism4.7. Problems5. The canonical ensemble5.1. A system in contact with a heat bath5.2. The partition function5.3. Definition of the entropy in the canonical ensemble5.4. The bridge to thermodynamics through Z5.5. The condition for thermal equilibrium5.6. Thermodynamic quantities from In(Z)5.7. Two-level System5.8. Single particle in a one-dimensional box5.9. Single particle in a three dimensional box5.10. Expressions for heat and work5.11. Rotational energy levels for diatomic molecules5.12. Vibrational energy levels for diatomic molecules5.13. Factorizing the partition function5.14. Equipartitiion theory5.15. Minimizing the free energy5.16. Problems6. Identical particles6.1. Identical particles6.2. Symmetric and antisymmetric wavefunctions6.3. Bose particles or bosons6.4. Fermi particles or fermions6.5. Calculating the partition function for identicle particles6.6. Spin6.7. Identical particles localized on lattice sites6.8. Identicle particles in a molecule6.9. Problems7. Maxwell distribution of molecular speeds7.1. The probability that a particle is in a quantum state7.2. Density of states in k space7.3. Single-particle density of states in energy7.4. The distribution of speeds of particles in a classical gas7.5. Molecular beams7.6. Problems8. Planck's distribution8.1. Black-body radiation8.2. The Rayleigh-Jeans theory8.3. Planck's distribution8.4. Waves as particles8.5. Derivation of the Planck distribution8.6. The free energy8.7. Einstein's model of vibrations in a solid8.8. Debye's model of vibrations in a solid8.9. Solid and vapour in equilibrium8.10. Cosmic background radiation8.11. Problems9. Systems with variable numbers of particles9.1. Systems with variable number of particles9.2. The condition for chemical equilibrium9.3. The approach to chemical equilibrium9.4. The chemical potential9.5. Reactions9.6. External chemical potential9.7. The grand canonical ensemble9.8. Absorption of atoms on surface sites9.9. The grand potential9.10. Problems10. Fermi and Bose particles10.1. Introduction10.2. The stastical mechanics of identical particles10.3. The thermodynamic properties of a Fermi gas10.4. Examples of Fermi systems10.5. A non-interacting Bose gas10.6. Problems11. Phase transitions11.1. Phases11.2. Thermodynamic potential11.3. Approximation11.4. First-order phase transition11.5. Clapeyron equation11.6. Phase separation11.7. Phase separation in mixtures11.8. Liquid gas system11.9. Problems12. Continuous phase transitions12.1. Introduction12.2. Ising model12.3. Order parameter12.4. Landau theory12.5. Symmetry-breaking field12.6. Critical exponents12.7. Problems13. Ginzburg Landau theory13.1. Ginzburg Landau theory13.2. Ginzburg criterion13.3. Surface tension13.4. Nucleation of droplets13.5. Superfluidity13.6. Order parameter13.7. Circulation13.8. Vortices13.9. Charged superfluids13.10. Quantization of flux13.11. ProblemsA. Thermodynamics in a magnetic fieldB. Useful integralsC. The quantum treatment of a diatomic moleculeD. Travelling wavesE. Partial differentials and thermodynamicsF. Van der Waals equationG. Answers to problemsH. Physical constantsBibliographyIndex

Editorial Reviews

On the first edition: "Introductory Statistical Mechanics is clear and crisp and takes advantage of the best parts of the many approaches to the subject." --Physics Today