An introduction to thermodynamics and statistical mechanics PDF
Preview An introduction to thermodynamics and statistical mechanics
This page intentionally left blank An Introduction to Thermodynamics and Statistical Mechanics, Second Edition Thisintroductorytextbookforstandardundergraduatecoursesin thermodynamicshasbeencompletelyrewrittentoexploreagreaternumberof topicsmoreclearlyandconcisely.Startingwithanoverviewofimportant quantumbehaviors,thebookteachesstudentshowtocalculateprobabilitiesin ordertoprovideafirmfoundationforlaterchapters.Itthenintroducestheideas of“classicalthermodynamics”--internalenergy,interactions,entropy,andthe fundamentalsecondlaw.Theseideasareexploredbothingeneralandasthey areappliedtomorespecificprocessesandinteractions.Theremainderofthe bookdealswith“statisticalmechanics”--thestudyofsmallsystemsinteracting withhugereservoirs. ThechangesinthisSecondEditionhavebeenmadeasaresultofmorethan10 yearsofclassroomtestingandfeedbackfromstudents.Tohelpstudentsreview theimportantconceptsandtesttheirnewlygainedknowledge,eachtopicends withaboxedsummaryofideasandresults.Everychapterhasnumerous homeworkproblems,coveringabroadrangeofdifficulties.Answersaregiven toodd-numberedproblems,andsolutionstoeven-numberedproblemsare availabletoinstructorsatwww.cambridge.org/9780521865579. K S isaprofessorofphysicsatCaliforniaPolytechnicState Universityandhasworkedtherefor32years.Hehasspenttimeatthe UniversityofWashington,Harvard,theUniversityofNorthCarolina,andthe UniversityofMichigan.AswellashavingwrittentheFirstEditionof IntroductiontoThermodynamicsandStatisticalMechanics,hehasalsowritten booksonoceanscience. An Introduction to Thermodynamics and Statistical Mechanics Second Edition Keith Stowe California Polytechnic State University CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521865579 © K. Stowe 2007 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2007 ISBN-13 978-0-511-27406-0 eBook (EBL) ISBN-10 0-511-27406-8 eBook (EBL) ISBN-13 978-0-521-86557-9 hardback ISBN-10 0-521-86557-3 hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Preface page vii Listofconstants,conversions,andprefixes xii PartI Settingthescene 1 1 Introduction 3 PartII Smallsystems 23 2 Statisticsforsmallsystems 25 3 Systemswithmanyelements 40 PartIII Energyandthefirstlaw 63 4 Internalenergy 65 5 Interactionsbetweensystems 79 PartIV Statesandthesecondlaw 99 6 Internalenergyandthenumberofaccessiblestates 101 7 Entropyandthesecondlaw 117 8 Entropyandthermalinteractions 135 PartV Constraints 153 9 Naturalconstraints 155 10 Models 186 11 Choiceofvariables 210 12 Specialprocesses 226 13 Engines 252 14 Diffusiveinteractions 287 PartVI Classicalstatistics 327 15 Probabilitiesandmicroscopicbehaviors 329 16 Kinetictheoryandtransportprocessesingases 352 17 Magneticpropertiesofmaterials 369 18 Thepartitionfunction 382 v vi Contents PartVII Quantumstatistics 399 19 Introductiontoquantumstatistics 401 20 Quantumgases 422 21 Blackbodyradiation 438 22 Thethermalpropertiesofsolids 457 23 Theelectricalpropertiesofmaterials 477 24 Lowtemperaturesanddegeneratesystems 504 Appendices 531 Furtherreading 537 Problemsolutions 538 Index 551 Preface Goals Thesubjectofthermodynamicswasbeingdevelopedonapostulatorybasislong before we understood the nature or behavior of the elementary constituents of matter.Aswebecamemorefamiliarwiththeseconstituents,wewerestillslowto placeourtrustinthe“new”fieldofquantummechanics,whichwastellingusthat their behaviors could be described correctly and accurately using probabilities andstatistics. Theinfluenceofthishistoricalsequencehaslingeredinourtraditionalther- modynamics curriculum. Until recently, we continued to teach an introductory courseusingthemoreformalandabstractpostulatoryapproach.Now,however, thereisagrowingfeelingthatthestatisticalapproachismoreeffective.Itdemon- stratesthefirmphysicalandstatisticalbasisofthermodynamicsbyshowinghow thepropertiesofmacroscopicsystemsaredirectconsequencesofthebehaviors oftheirelementaryconstituents.Anaddedadvantageofthisapproachisthatitis easilyextendedtoincludesomestatisticalmechanicsinanintroductorycourse. Itgivesthestudentabroaderspectrumofskillsaswellasabetterunderstanding ofthephysicalbases. Thisbookisintendedforuseinthestandardjuniororseniorundergraduate courseinthermodynamics,anditassumesnopreviousknowledgeofthesubject. Itrytointroducethesubjectassimplyandsuccinctlyaspossible,withenough applicationstoindicatetherelevanceoftheresultsbutnotsomanyasmightrisk losingthestudentindetails.Therearemanyadvancedbooksofhighqualitythat canhelptheinterestedstudentprobemoredeeplyintothesubjectanditsmore specializedapplications. I try to tie everything straight to fundamental concepts, and I avoid “slick tricks”andthe“pyramiding”ofresults.Iremainfocusedonthebasicideasand physicalcauses,becauseIbelievethiswillhelpstudentsbetterunderstand,retain, andapplythetoolsandresultsthatwedevelop. Active learning Ithinkthatreallearningmustbeanactiveprocess.Itisimportantforthestudent toapplynewknowledgetospecificproblemsassoonaspossible.Thisshouldbea vii viii Preface dailyactivity,andproblemsshouldbeattemptedwhiletheknowledgeisstillfresh. Aroutineoffrequent,timely,andshortproblem-solvingsessionsisfarsuperior toafewinfrequentproblem-solvingmarathons.Forthisreason,attheendofeach chapterthetextincludesaverylargenumberofsuggestedhomeworkproblems, whichareorganizedbysection.Solutionstotheodd-numberedproblemsareat theendofthebookforinstantfeedback. Active learning can also be encouraged by streamlining the more passive components.Thesoonerthestudentunderstandsthetextmaterial,thesoonerhe orshecanapplyit.Forthisreason,IhaveputthetopicsinwhatIbelievetobethe mostlearning-efficientorder,andIexplaintheconceptsassimplyandclearlyas possible.Summariesarefrequentandareincludedwithinthechapterswherever Ithinkwouldbehelpfultoafirst-timestudentwrestlingwiththeconcepts.They arealsoshadedforeasyidentification.Hopefully,thisstreamliningofthepassive aspectsmightallowmoretimeforactiveproblemsolving. Changes in the second edition Theentirebookhasbeenrewritten.Myprimaryobjectiveforthesecondedition hasbeentoexploremoretopics,morethoroughly,moreclearly,andwithfewer words.ToaccomplishthisIhavewrittenmoreconcisely,combinedrelatedtopics, and reduced repetition. The result is a modest reduction in text, in spite of the broadenedcoverageoftopics. InadditionIwantedtocorrectwhatIconsideredtobethetwobiggestproblems withthefirstedition:thelargenumberofuncorrectedtyposandanincomplete description of the chemical potential. A further objective was to increase the number and quality of homework problems that are available for the instructor orstudenttoselectfrom.Theserangeindifficultyfromwarm-upstochallenges. Inthiseditionthenumberofhomeworkproblemshasnearlydoubled,averaging around40perchapter.Inaddition,solutions(andoccasionalhints)totheodd- numberedproblemsaregivenatthebackofthebook.Myexperiencewithstudents atthislevelhasbeenthatsolutionsgivequickandefficientfeedback,encouraging thosewhoaredoingthingscorrectlyandhelpingtoguidethosewhostumble. Thefollowinglistexpandsuponthemoreimportantnewinitiativesandfea- turesinthiseditioninorderoftheirappearance,withthechaptersandsections indicatedinparentheses. (cid:1) Fluctuationsinobservables,suchasenergy,temperature,volume,numberofparticles, etc.(Sections3A,3C,7C,9B,19A) (cid:1) Improveddiscussionandillustrationsofthechemicalpotential(Sections5C,8A,9E, 14A) (cid:1) The explicit dependence of the number of accessible states on the system’s internal energy,volume,andnumberofparticles(Chapter6) (cid:1) Behaviorsnearabsolutezero(Sections9H,24A,24B)
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