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Thermal Physics Clear and reader-friendly, this is an ideal textbook for students seeking an up-to-date introduction to thermal physics. Written by an experienced teacher and extensively class-tested, Thermal Physics provides a comprehensive grounding in thermodynamics, statistical mechanics, and kinetic theory. A key feature of this text is its readily accessible introductory chapters, which begin with a review of fundamental ideas. Entropy, conceived microscopically and statistically, and the Second Law of Thermodynamics are introduced early in the book. Throughout, new topics are built on a conceptual foundation of four linked elements: entropy and the Second Law, the canonical probability distribution, the partition function, and the chemical potential. As well as providing a solid preparation in the basics of the subject, the text goes on to explain exciting recent developments such as Bose-Einstein condensation and critical phenomena. Key equations are highlighted throughout, and each chapter contains a summary of essential ideas and an extensive set of problems of varying degrees of difficulty. A solutions manual is available for instructors. Suitable for both undergraduates and graduates in physics and astronomy. Born in 1936 and educated at Harvard and Princeton Universities, Ralph Baierlein is currently Charlotte Ayres Professor of Physics at Wesleyan University, Middletown, Connecticut. He is a fellow of the American Physical Society and in 1998 received a Distinguished Service Citation from the American Association of Physics Teachers. He is also author of other university textbooks including Atoms and Information Theory, Newtonian Dynamics, and Newton to Einstein: The Trail of Light. Downloaded from https:/www.cambridge.org/core. University of Exeter, on 19 Mar 2017 at 08:52:53, subject to the Cambridge Core terms of use, available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511840227 Downloaded from https:/www.cambridge.org/core. University of Exeter, on 19 Mar 2017 at 08:52:53, subject to the Cambridge Core terms of use, available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511840227 Thermal Physics RALPH BAIERLEIN Wesleyan University CAMBRIDGE UNIVERSITY PRESS Downloaded from https:/www.cambridge.org/core. University of Exeter, on 19 Mar 2017 at 08:52:53, subject to the Cambridge Core terms of use, available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511840227 CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 2RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521590822 © Ralph Baierlein 1999 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1999 Sixth printing 2005 A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Baierlein, Ralph. Thermal physics / Ralph Baierlein. p. cm. ISBN 0 521 59082 5 1. Thermodynamics. 2. Entropy. 3. Statistical mechanics. I. Title. QC311.B293 1999 536’.7-dc21 98-38617 CIP ISBN-13 978-0-521-59082-2 hardback ISBN-10 0-521-59082-5 hardback ISBN-13 978-0-521-65838-6 paperback ISBN-10 0-521-65838-1 paperback Transferred to digital printing 2006 Downloaded from https:/www.cambridge.org/core. University of Exeter, on 19 Mar 2017 at 08:52:53, subject to the Cambridge Core terms of use, available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511840227 Contents Preface xi 1 Background 1.1 Heating and temperature 1 1.2 Some dilute gas relationships 4 1.3 The First Law of Thermodynamics 1.4 Heat capacity 11 1.5 An adiabatic process 13 1.6 The meaning of words 16 1.7 Essentials 18 Further reading 21 Problems 21 2 The Second Law of Thermodynamics 2.1 Multiplicity 24 2.2 The Second Law of Thermodynamics 28 2.3 The power of the Second Law 29 2.4 Connecting multiplicity and energy transfer by heating 31 2.5 Some examples 35 2.6 Generalization 39 2.7 Entropy and disorder 44 2.8 Essentials 45 Further reading 46 Problems 47 Entropy and Efficiency 3.1 The most important thermodynamic cycle: the Carnot cycle 57 3.2 Maximum efficiency 55 3.3 A practical consequence 59 3.4 Rapid change 60 Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 19 Mar 2017 at 08:59:24, subject to the Cambridge Core terms of use, available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511840227 vi Contents 3.5 The simplified Otto cycle 62 3.6 More about reversibility 67 3.7 Essentials 69 Further reading 70 Problems 71 4 Entropy in Quantum Theory 4.1 The density of states 75 4.2 The quantum version of multiplicity 80 4.3 A general definition of temperature 80 4.4 Essentials 86 Problems 87 5 The Canonical Probability Distribution 5.1 Probabilities 89 5.2 Probabilities when the temperature is fixed 91 5.3 An example: spin \ft paramagnetism 94 5.4 The partition function technique 96 5.5 The energy range dE 99 5.6 The ideal gas, treated semi-classically 101 5.7 Theoretical threads 109 5.8 Essentials 109 Further reading 111 Problems 112 6 Photons and Phonons 6.1 The big picture 116 6.2 Electromagnetic waves and photons 118 6.3 Radiative flux 123 6.4 Entropy and evolution (optional) 128 6.5 Sound waves and phonons 130 6.6 Essentials 139 Further reading 141 Problems 141 7 The Chemical Potential 7.1 Discovering the chemical potential 148 7.2 Minimum free energy 155 Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 19 Mar 2017 at 08:59:24, subject to the Cambridge Core terms of use, available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511840227 Contents vii 7.3 A lemma for computing JU 156 1A Adsorption 157 7.5 Essentials 160 Further reading 161 Problems 162 8 The Quantum Ideal Gas 8.1 Coping with many particles all at once 166 8.2 Occupation numbers 168 8.3 Estimating the occupation numbers 170 8.4 Limits: classical and semi-classical 173 8.5 The nearly classical ideal gas (optional) 175 8.6 Essentials 178 Further reading * 179 Problems 180 9 Fermions and Bosons at Low Temperature 9.1 Fermions at low temperature 182 9.2 Pauli paramagnetism (optional) 192 9.3 White dwarf stars (optional) 194 9.4 Bose-Einstein condensation: theory 199 9.5 Bose-Einstein condensation: experiments * 205 9.6 A graphical comparison 209 9.7 Essentials 212 Further reading 214 Problems 215 10 The Free Energies 10.1 Generalities about an open system 222 10.2 Helmholtz free energy 225 10.3 More on understanding the chemical potential 226 10.4 Gibbs free energy 230 10.5 The minimum property 233 10.6 Why the phrase "free energy"? 234 10.7 Miscellany 236 10.8 Essentials 238 Further reading 239 Problems 240 Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 19 Mar 2017 at 08:59:24, subject to the Cambridge Core terms of use, available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511840227 viii Contents 11 Chemical Equilibrium 11.1 The kinetic view 244 11.2 A consequence of minimum free energy 246 11.3 The diatomic molecule 250 11.4 Thermal ionization 25 7 11.5 Another facet of chemical equilibrium 260 11.6 Creation and annihilation 262 11.7 Essentials 264 Further reading 266 Problems 266 12 Phase Equilibrium 12.1 Phase diagram 270 12.2 Latent heat 273 12.3 Conditions for coexistence 276 12.4 Gibbs-Duhem relation 279 12.5 Clausius-Clapeyron equation 280 12.6 Cooling by adiabatic compression (optional) 282 12.7 Gibbs' phase rule (optional) 290 12.8 Isotherms 291 12.9 Van der Waals equation of state 293 12.10 Essentials 300 Further reading 301 Problems 301 13 The Classical Limit 13.1 Classical phase space 306 13.2 The Maxwellian gas 309 13.3 The equipartition theorem 314 13.4 Heat capacity of diatomic molecules 318 13.5 Essentials 320 Further reading 322 Problems 322 14 Approaching Zero 14.1 Entropy and probability 32 7 14.2 Entropy in paramagnetism 329 14.3 Cooling by adiabatic demagnetization 331 14 A The Third Law of Thermodynamics 33 7 Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 19 Mar 2017 at 08:59:24, subject to the Cambridge Core terms of use, available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511840227 Contents ix 14.5 Some other consequences of the Third Law 341 14.6 Negative absolute temperatures 343 14.7 Temperature recapitulated 347 14.8 Why heating increases the entropy. Or does it? 349 14.9 Essentials 351 Further reading 352 Problems 353 15 Transport Processes 15.1 Mean free path 356 15.2 Random walk 360 15.3 Momentum transport: viscosity 362 15.4 Pipe flow 366 15.5 Energy transport: thermal conduction 367 15.6 Time-dependent thermal conduction 369 15.7 Thermal evolution: an example 372 15.8 Refinements 375 15.9 Essentials 377 Further reading 3 78 Problems 378 16 Critical Phenomena 16.1 Experiments 382 16.2 Critical exponents 388 16.3 Ising model 389 16.4 Mean field theory 392 16.5 Renormalization group 397 16.6 First-order versus continuous 407 16.7 Universality 409 16.8 Essentials 414 Further reading 415 Problems 415 Epilogue 419 Appendix A Physical and Mathematical Data 420 Appendix B Examples of Estimating Occupation Numbers 426 Appendix C The Framework of Probability Theory 428 Appendix D Qualitative Perspectives on the van der Waals Equation 435 Index 438 Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 19 Mar 2017 at 08:59:24, subject to the Cambridge Core terms of use, available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511840227 Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 19 Mar 2017 at 08:59:24, subject to the Cambridge Core terms of use, available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511840227