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Sandeep Sharma Thermal and Statistical Physics Concepts and Applications Thermal and Statistical Physics Sandeep Sharma Thermal and Statistical Physics Concepts and Applications SandeepSharma DepartmentofPhysics GuruNanakDevUniversity Amritsar,Punjab,India ISBN978-3-031-07684-8 ISBN978-3-031-07685-5 (eBook) https://doi.org/10.1007/978-3-031-07685-5 JointlypublishedwithANEBooksPvt.Ltd. Inadditiontothisprintededition,thereisalocalprintededitionofthisworkavailableviaAneBooksin SouthAsia(India,Pakistan,SriLanka,Bangladesh,NepalandBhutan)andAfrica(allcountriesinthe Africansubcontinent). ISBNoftheCo-Publisher’sedition:9789390658268 ©TheAuthor(s)2022 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublishers,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishersnortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublishersremainneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Dedicated tomy studentsandShivansh Preface This book is an outcome of lectures that I have delivered to bachelor and master students at Guru Nanak Dev University, Amritsar, Punjab, India. The content presentedinthebookisclassroomtestedandvariousstudentshavebenefitedfrom it. The primary objective of this book is to introduce the fundamental concepts of thermal and statistical physics and their use in understanding various problems. Theconceptsarepresentedinaverysimplewaysothatreadercanbuildupafirm foundation in the subject. In Chap. 1, starting with some historical facts we introduce the main subject of classical thermodynamics. The concept of thermodynamic limit, intensive and extensive variables, and perfect and imperfect differentials are introduced. In Chap. 2, we introduce the Zeroth law of thermodynamics, concept of work and sign convention. This chapter also highlights and clarifies the use of different sign conventions, and emphasizes that both lead to the same results. The chapter includes a discussion of the first law of thermodynamics and ends with a description of heat and the idea of heat capacity. Chapter 3 deals with the crucial second law of thermodynamics. The idea of a Carnot heat engine is introduced in this chapter. Various statements of the second lawofthermodynamicswhichoriginatefromthediscussionoftheheatengineare introduced. At the end of this chapter, a description of the thermodynamic scale of temperature and its equivalence with the ideal gas scale is presented. Chapter 4 begins with the crucial concept of entropy. This is followed by various illustrations chosen from daily life. The important concept of free expansion is also included in this chapter. This chapter ends with a discussion on the third law of thermodynamics. In Chap. 5, various thermodynamic potentials, such as the internal energy, enthalpy,HelmholtzfunctionandGibbsfunction,arepresented.Aqualitativedis- cussion on free energy, Maxwell’s relations, Clausius–Clapeyron equation, TdS equations and magneto caloric effects is also included in this chapter. Chapter 6 presents the kinetic theory of gases along with the Maxwell– Boltzmannlawofdistributionofvelocities.TheDopplerbroadening,andZartman and Stern’s experiments are included in this chapter. At the end of this chapter, we present degrees of freedom, evaluation of mean free path and discussion on various transport phenomena. vii viii Preface Chapters 7 and 8 deal with real gases. In Chap. 7, deviation of ideal gas behaviour is presented. This is followed by the Van der Waals equation of state, Andrew’sexperimentandevaluationofcriticalconstantsofarealgas.InChap.8, the Joule expansion and Joule–Kelvin expansions are discussed. Chapter 9 is devoted to the theory of radiations. The chapter covers various aspects of Black body radiation spectra, Wien’s displacement law, Newton’s law of cooling, Rayleigh–Jeans law and Planck’s law are covered in detail. Chapter 10 of the book is devoted to the introduction of basic concepts in statistical mechanics. In this chapter, we introduce the idea of phase space, dis- tinction between microstates and macrostates. Thermodynamic probability and its derivation for three different cases of Maxwell–Boltzmann, Fermi–Dirac and Bose–Einstein statistics are discussed. Amritsar, India Sandeep Sharma UGC Approved Syllabus for Choice-Based Credit System Laws of Thermodynamics Thermodynamic Description of a system: Zeroth law of thermodynamics and temperature; First law and internal energy, conversion of heat into work, various thermodynamical processes; Applications of First Law: General Relation between C and C , Work Done during Isothermal and Adiabatic Processes, P V Compressibility and Expansion Coefficient, Reversible and Irreversible processes, Second law and Entropy, Carnot’s cycle and Carnot’s theorem, Entropy changes inreversibleandirreversibleprocesses,Entropy–Temperaturediagrams,Thirdlaw of thermodynamics and Unattainability of absolute zero. [22Lectures] Thermodynamic Potentials Enthalpy, Gibbs, Helmholtz and Internal Energy functions, Maxwell’s relations and applications, Joule–Thompson effect, Clausius–Clapeyron equation and Expression for (C −C ), C /C , TdS equations. P V P V [10Lectures] Kinetic Theory of Gases Derivation of Maxwell’s law of distribution of velocities and its experimental verification,Meanfreepath(Zerothorder);TransportPhenomena:Viscosity,Con- duction and Diffusion (for vertical case), Law of equipartition of energy (no derivation, qualitative description only) and its applications to specific heat of gases; monoatomic and diatomic gases. [10Lectures] ix x UGCApprovedSyllabusforChoice-BasedCreditSystem Theory of Radiation Blackbody radiation, Spectral distribution, Concept of Energy Density, Derivation ofPlanck’slaw,DeductionofWien’sdistributionlaw,Rayleigh–Jeanslaw,Stefan– Boltzmann law and Wien’s displacement law from Planck’s law. [6Lectures] Statistical Mechanics Maxwell–Boltzmannlaw,distributionofvelocity,Quantumstatistics,Phasespace, Fermi–Diracdistributionlaw,electrongas,Bose–Einsteindistributionlaw,photon gas and comparison of three statistics. [12Lectures] Thermal and Statistical Physics—Concepts and Applications Salient Features According to the latest syllabus as per UGC guidelines; Inclusion of topics related to NET and GATE examinations; Inclusion of Numerical problems with solutions from the last 20 years of examinations (NET-JRF, GATE, JAM, JEST, etc.); Various illustrations from daily life; Enriched with various diagrams, illustrations and mnemonics; More than 380 solved problems including 240 MCQ type questions; Covers newly introduced topics like radiation, cooling of real gases. Contents 1 Introduction ........................................................ 1 1.1 Origin of Thermodynamics .................................. 1 1.2 A Macroscopic Approach .................................... 1 1.3 The Thermodynamic Limit and Its Consequences ............ 2 1.3.1 Intensive and Extensive Variables .................... 3 1.4 System Versus Surrounding .................................. 3 1.4.1 A System in Thermodynamic Equilibrium ........... 4 1.4.2 Thermodynamic Variables or Functions of State ...... 4 1.4.3 Equation of a State .................................. 5 1.4.4 Physical Meaning of dV, dP and dT ................. 6 1.5 Thermodynamic Reversibility ................................ 8 1.6 A Few Important Mathematical Results ...................... 8 1.6.1 The Reciprocal Theorem ............................ 8 1.6.2 Reciprocity Theorem ................................ 9 1.6.3 Perfect Differential .................................. 10 1.7 Solved Problems ............................................. 10 1.8 Multiple Choice Questions ................................... 13 2 TheLawsofThermodynamics ...................................... 17 2.1 The Zeroth Law ............................................. 17 2.2 Concept of Work and Sign Convention ....................... 18 2.2.1 The Sign Convention ................................ 19 2.2.2 P-V Diagrams ....................................... 20 2.2.3 Path Dependence of Work Done ..................... 21 2.2.4 Path Dependence of Heat-Transfer ................... 22 2.3 Work Done in Various Systems .............................. 23 2.3.1 Work Done in Changing the Area of a Surface Film ................................................ 23 2.3.2 Work Done in Changing the Area of a Liquid Drop ................................................ 24 2.4 Historical Background Related to First Law of Thermodynamics .......................................... 25 2.5 First Law of Thermodynamics ............................... 27 2.5.1 Applying First Law to Various Systems .............. 29 xi