Theoretical Physics 5: Thermodynamics PDF
Preview Theoretical Physics 5: Thermodynamics
Wolfgang Nolting Theoretical Physics 5 Thermodynamics Theoretical Physics 5 Wolfgang Nolting Theoretical Physics 5 Thermodynamics 123 WolfgangNolting Inst.Physik Humboldt-UniversitätzuBerlin Berlin,Germany ISBN978-3-319-47909-5 ISBN978-3-319-47910-1 (eBook) DOI10.1007/978-3-319-47910-1 LibraryofCongressControlNumber:2016943655 ©SpringerInternationalPublishingAG2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland General Preface TheninevolumesoftheseriesBasicCourse:TheoreticalPhysicsarethoughttobe textbookmaterialforthestudyofuniversitylevelphysics.Theyareaimedtoimpart, in a compact form, the most important skills of theoretical physics which can be usedasbasisforhandlingmoresophisticatedtopicsandproblemsintheadvanced study of physics as well as in the subsequent physics research. The conceptual designofthepresentationisorganizedinsuchawaythat ClassicalMechanics(volume1) AnalyticalMechanics(volume2) Electrodynamics(volume3) SpecialTheoryofRelativity(volume4) Thermodynamics(volume5) are considered as the theory part of an integrated course of experimental and theoretical physics as is being offered at many universities starting from the first semester.Therefore,thepresentationisconsciouslychosentobeveryelaborateand self-contained,sometimessurelyatthe costofcertainelegance,sothatthecourse is suitableevenforself-study,at firstwithoutanyneedof secondaryliterature.At anystage,nomaterialisusedwhichhasnotbeendealtwithearlierinthetext.This holds in particular for the mathematical tools, which have been comprehensively developed starting from the school level, of course more or less in the form of recipes,suchthatrightfromthebeginningofthestudy,onecansolveproblemsin theoreticalphysics. The mathematicalinsertionsare always then pluggedin when theybecomeindispensabletoproceedfurtherintheprogramoftheoreticalphysics. It goes without saying that in such a context, not all the mathematical statements canbeprovedandderivedwithabsoluterigor.Instead,sometimesareferencemust be made to an appropriate course in mathematics or to an advanced textbook in mathematics. Nevertheless, I have tried for a reasonably balanced representation so that the mathematical tools are not only applicable but also appear at least “plausible”. v vi GeneralPreface Themathematicalinterludesareofcoursenecessaryonlyinthefirstvolumesof thisseries,whichincorporatemoreorlessthematerialofabachelorprogram.Inthe secondpartoftheserieswhichcomprisesthemodernaspectsoftheoreticalphysics, QuantumMechanics:Basics(volume6) QuantumMechanics:MethodsandApplications(volume7) StatisticalPhysics(volume8) Many-BodyTheory(volume9), mathematical insertions are no longer necessary. This is partly because, by the time one comes to this stage, the obligatory mathematics courses one has to take in order to study physics would have provided the required tools. The fact that training in theory has already started in the first semester itself permits inclusion of parts of quantum mechanics and statistical physics in the bachelor program itself. It is clear that the content of the last three volumes cannot be part of an integrated course but rather the subject matter of pure theory lectures. This holds in particular for Many-Body Theory which is offered, sometimes under different names,e.g.,AdvancedQuantumMechanics,in the eighthorso semester ofstudy. In this part, new methods and concepts beyond basic studies are introduced and discussed which are developed in particular for correlated many particle systems whichinthemeantimehavebecomeindispensableforastudentpursuingamaster’s orahigherdegreeandforbeingabletoreadcurrentresearchliterature. In all the volumes of the series Theoretical Physics, numerous exercises are included to deepen the understanding and to help correctly apply the abstractly acquired knowledge. It is obligatory for a student to attempt on his own to adapt and apply the abstract concepts of theoretical physics to solve realistic problems. Detailedsolutionstotheexercisesaregivenattheendofeachvolume.Theideais tohelpastudenttoovercomeanydifficultyataparticularstepofthesolutionorto checkone’sowneffort.Importantlythesesolutionsshouldnotseducethestudentto followtheeasywayoutasasubstituteforhisowneffort.Attheendofeachbigger chapter,Ihaveaddedself-examinationquestionswhichshallserveasaself-testand maybeusefulwhilepreparingforexaminations. I should not forget to thank all the people who have contributed one way or another to the success of the book series. The single volumes arose mainly from lectures which I gave at the universities of Muenster, Wuerzburg, Osnabrueck, and Berlin (Germany),Valladolid (Spain), and Warangal(India). The interest and constructive criticism of the students provided me the decisive motivation for preparing the rather extensive manuscripts. After the publication of the German version,Ireceivedalotofsuggestionsfromnumerouscolleaguesforimprovement, and this helped to further develop and enhance the concept and the performance of the series. In particular, I appreciate very much the support by Prof. Dr. A. Ramakanth,a long-standingscientific partnerand friend,who helpedme in many respects,e.g.,whatconcernsthecheckingofthetranslationoftheGermantextinto thepresentEnglishversion. GeneralPreface vii SpecialthanksareduetotheSpringercompany,inparticulartoDr.Th.Schneider and his team. I remember many useful motivations and stimulations. I have the feelingthatmybooksarewelltakencareof. Berlin,Germany WolfgangNolting August2016 Preface to Volume 5 The main goal of the present volume 5 (Thermodynamics) is exactly the same as that of the total course on Theoretical Physics. It is thought to be accompanying textbook material for the study of university-level physics. It is aimed to impart, in a compact form, the most important skills of theoretical physics which can be usedasbasisforhandlingmoresophisticatedtopicsandproblemsintheadvanced study of physics as well as in the subsequent physics research. It is presented in such a way that it enables self-study without the need for a demanding and laboriousreferenceto secondaryliterature. For the understandingof the text, it is onlypresumedthatthereaderhasagoodgraspofwhathasbeenelaboratedinthe precedingvolumes1,2,3,and4.Mathematicalinterludesarealwayspresentedin a compact and functional form and practiced when they appear indispensable for the further development of the theory. Such mathematical insertions, though, are becoming of course decreasingly necessary with the increasing volume number. For the whole text, it holds that I had to focus on the essentials, presenting them in a detailed and elaborate form, sometimes consciously sacrificing certain elegance.Itgoeswithoutsayingthat,afterthebasiccourse,secondaryliteratureis neededtodeepentheunderstandingofphysicsandmathematics.Thermodynamics belongstotheclassicaltheoriesbutwouldthematicallybebetteroffasapreludeto StatisticalMechanics.Thelattercanbeoffered,however,asmodern,nonclassical theory (Quantum Statistics) only at a later stage of the study, namely, after we have dealt with the Quantum Mechanics (volumes 6 and 7). The classical phenomenologicalThermodynamics takes its concept formation directly from the experimentanddoesthereforenotneed,incontrasttotheQuantumStatistics,any quantum-mechanical element. As a rule, it is a module of the bachelor program in physics and has therefore to be integrated into the first (classical) part of this course on theoretical physics. The exact position of Thermodynamics in such a course is, however,notunique.It can also be offeredbefore the Electrodynamics. Thermodynamicsis, asascience ofheat,aclassicalphenomenologicaltheoryand fortheunderstandingofwhich,physicaltermsliketemperatureandheathavetobe introduced.Thesequantitiesare reasonablydefinableonlyformacroscopicmany- particlesystemsbeingcompletelymeaninglessforasingleparticle.Thefulltheory ix x PrefacetoVolume5 of Thermodynamicsis based on a few fundamentaltheorems or laws, which have to be considered here as theoretically non-provable but experimentally unrefuted empiricalfacts.Astothesetheorems,aswellastothetermstemperatureandheat, we have to content ourselves, in the framework of thermodynamics, to a certain degree, with an intuitive self-understanding. A systematic reasoning is possible only with Statistical Mechanics (volume 8) which is thus to be considered as complementaryto thermodynamics.It is consistent with, at least in its version as QuantumStatistics, theprinciplesofquantummechanicswhichwillbedeveloped in the volumes 6 and 7. This volume on Thermodynamics arose from lectures I gaveattheGermanuniversitiesinMuenster,Wuerzburg,andBerlin.Theanimating interestofthestudentsinmylecturenoteshasinducedmetopreparethetextwith special care. The present one as well as the other volumes are thought to be the textbookmaterialforthestudyofbasicphysics,primarilyintendedforthestudents rather than for the teachers. I am thankful to the Springer company,especially to Dr. Th. Schneider, for accepting and supporting the concept of my proposal. The collaborationwasalwaysdelightfulandveryprofessional.Adecisivecontribution tothebookwasprovidedbyProf.Dr.A.RamakanthfromtheKakatiyaUniversity ofWarangal(India).Hedeservesalotofthanks! Berlin,Germany WolfgangNolting September2016 Contents 1 BasicConcepts ............................................................... 1 1.1 ThermodynamicSystems.............................................. 2 1.2 State,Equilibrium ..................................................... 4 1.3 TheConceptofTemperature.......................................... 6 1.4 EquationsofState ..................................................... 7 1.4.1 IdealGas....................................................... 8 1.4.2 VanderWaalsGas ............................................ 10 1.4.3 IdealParamagnet.............................................. 14 1.4.4 WeissFerromagnet............................................ 15 1.5 Work.................................................................... 18 1.6 Exercises............................................................... 22 1.7 Self-ExaminationQuestions .......................................... 26 2 LawsofThermodynamics................................................... 29 2.1 FirstLawofThermodynamics,InternalEnergy ..................... 29 2.2 HeatCapacities ........................................................ 33 2.3 Adiabatics,Isotherms.................................................. 35 2.4 SecondLawofThermodynamics..................................... 38 2.5 CarnotCycle........................................................... 41 2.6 Absolute,ThermodynamicTemperatureScale....................... 45 2.7 EntropyasStateQuantity ............................................. 48 2.8 SimpleConclusionsfromtheThermodynamicLaws................ 55 2.9 Exercises............................................................... 61 2.10 Self-ExaminationQuestions .......................................... 71 3 ThermodynamicPotentials ................................................. 75 3.1 ‘Natural’StateVariables .............................................. 75 3.2 LegendreTransformation ............................................. 77 3.3 HomogeneityRelations................................................ 81 3.4 TheThermodynamicPotentialsoftheIdealGas..................... 83 3.5 EntropyofMixing..................................................... 87 3.6 Joule-ThomsonEffect................................................. 91 xi
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