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Statistical Thermodynamics

466 Pages · 2014 · 4.11 MB · English

  • Statistical Thermodynamics

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    STATISTICAL THERMODYNAMICS: FUNDAMENTALS


    AND APPLICATIONS


    Statistical Thermodynamics: Fundamentals and Applications discusses the


    fundamentals and applications of statistical thermodynamics for beginning


    graduate students in the engineering sciences. Building on the prototypical


    Maxwell–Boltzmann method and maintaining a step-by-step development of


    thesubject,thisbookmakesfewpresumptionsconcerningstudents’previous


    exposure to statistics, quantum mechanics, or spectroscopy. The book begins


    with the essentials of statistical thermodynamics, pauses to recover needed


    knowledgefromquantummechanicsandspectroscopy,andthenmovesonto


    applications involving ideal gases, the solid state, and radiation. A full intro-


    duction to kinetic theory is provided, including its applications to transport


    phenomenaandchemicalkinetics.Ahighlightofthetextbookisitsdiscussion


    of modern applications, such as laser-based diagnostics. The book concludes


    withathoroughpresentationoftheensemblemethod,featuringitsuseforreal


    gases.Eachchapteriscarefullywrittentoaddressstudentdifficultiesinlearn-


    ingthischallengingsubject,whichisfundamentaltocombustion,propulsion,


    transportphenomena,spectroscopicmeasurements,andnanotechnology.Stu-


    dentsaremadecomfortablewiththeirnewknowledgebytheinclusionofboth


    exampleandpromptedhomeworkproblems.


    NormandM.LaurendeauistheRalphandBettyeBaileyProfessorofCombus-


    tionatPurdueUniversity.Heteachesatboththeundergraduateandgraduate


    levelsintheareasofthermodynamics,combustion,andengineeringethics.He


    conductsresearchinthecombustionsciences,withparticularemphasisonlaser


    diagnostics, pollutant formation, and flame structure. Dr. Laurendeau is well


    knownforhispioneeringresearchonthedevelopmentandapplicationofboth


    nanosecondandpicosecondlaser-inducedfluorescencestrategiestoquantita-


    tivespeciesconcentrationmeasurementsinlaminarandturbulentflames.He


    hasauthoredorcoauthoredover150publicationsinthearchivalscientificand


    engineeringliterature.ProfessorLaurendeauisaFellowoftheAmericanSoci-


    ety of Mechanical Engineers and a member of the Editorial Advisory Board


    forthepeer-reviewedjournalCombustionScienceandTechnology.


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    Statistical Thermodynamics


    Fundamentals and Applications


    NORMAND M. LAURENDEAU


    PurdueUniversity


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    Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo


    Cambridge University Press


    The Edinburgh Building, Cambridge ✏x00⇧ ⇧⇠x00, UK


    Published in the United States of America by Cambridge University Press, New York


    www.cambridge.org


    Information on this title: www.cambridge.org/9780521846356


    © Cambridge University Press 2005


    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 2005


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    Idedicatethisbooktomyparents,


    MauriceandLydiaRoyLaurendeau.


    Theirgiftofbountifulloveandsupport...


    Continuestofillmewiththejoyofdiscovery.


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    Contents


    Preface page xv


    1 Introduction 1


    1.1 TheStatisticalFoundationofClassicalThermodynamics 1


    1.2 AClassificationSchemeforStatisticalThermodynamics 3


    1.3 WhyStatisticalThermodynamics? 3


    PARTONE. FUNDAMENTALSOFSTATISTICAL


    THERMODYNAMICS


    2 ProbabilityandStatistics 7


    2.1 Probability:DefinitionsandBasicConcepts 7


    2.2 PermutationsandCombinations 10


    2.3 Probability Distributions: Discrete and Continuous 11


    2.4 TheBinomialDistribution 13


    2.5 ThePoissonDistribution 15


    2.6 TheGaussianDistribution 16


    2.7 CombinatorialAnalysisforStatisticalThermodynamics 18


    2.7.1 DistinguishableObjects 19


    2.7.2 IndistinguishableObjects 20


    ProblemSetI. ProbabilityTheoryandStatisticalMathematics


    (Chapter2) 23


    3 TheStatisticsofIndependentParticles 29


    3.1 EssentialConceptsfromQuantumMechanics 30


    3.2 TheEnsembleMethodofStatisticalThermodynamics 31


    3.3 TheTwoBasicPostulatesofStatisticalThermodynamics 32


    3.3.1 TheM–BMethod:SystemConstraintsandParticle


    Distribution 33


    3.3.2 TheM–BMethod:MicrostatesandMacrostates 33


    3.4 TheMostProbableMacrostate 35


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    viii Contents


    !


    3.5 Bose–EinsteinandFermi–DiracStatistics 37


    3.5.1 Bose–EinsteinStatistics 37


    3.5.2 Fermi–DiracStatistics 38


    3.5.3 TheMostProbableParticleDistribution 39


    3.6 EntropyandtheEquilibriumParticleDistribution 40


    3.6.1 TheBoltzmannRelationforEntropy 40


    3.6.2 IdentificationofLagrangeMultipliers 41


    3.6.3 TheEquilibriumParticleDistribution 42


    4 ThermodynamicPropertiesintheDiluteLimit 45


    4.1 TheDiluteLimit 45


    4.2 CorrectedMaxwell–BoltzmannStatistics 46


    4.3 TheMolecularPartitionFunction 47


    4.3.1 TheInfluenceofTemperature 49


    4.3.2 CriterionforDiluteLimit 50


    4.4 InternalEnergyandEntropyintheDiluteLimit 51


    4.5 AdditionalThermodynamicPropertiesintheDilute


    Limit 53


    4.6 TheZeroofEnergyandThermodynamicProperties 55


    4.7 IntensiveThermodynamicPropertiesfortheIdealGas 56


    Problem Set II. Statistical Modeling for Thermodynamics


    (Chapters 3–4) 59


    PARTTWO. QUANTUMMECHANICSANDSPECTROSCOPY


    5 BasicsofQuantumMechanics 69


    5.1 HistoricalSurveyofQuantumMechanics 69


    5.2 TheBohrModelfortheSpectrumofAtomicHydrogen 72


    5.3 ThedeBroglieHypothesis 76


    5.4 AHeuristicIntroductiontotheSchro¨dingerEquation 78


    5.5 ThePostulatesofQuantumMechanics 80


    5.6 TheSteady-StateSchro¨dingerEquation 83


    5.6.1 Single-ParticleAnalysis 84


    5.6.2 MultiparticleAnalysis 85


    5.7 TheParticleinaBox 86


    5.8 TheUncertaintyPrinciple 90


    5.9 IndistinguishabilityandSymmetry 92


    5.10 ThePauliExclusionPrinciple 94


    5.11 TheCorrespondencePrinciple 95


    6 QuantumAnalysisofInternalEnergyModes 97


    6.1 Schro¨dingerWaveEquationforTwo-ParticleSystem 97


    6.1.1 ConversiontoCenter-of-MassCoordinates 98


    6.1.2 SeparationofExternalfromInternalModes 99


    6.2 TheInternalMotionforaTwo-ParticleSystem 99


    6.3 TheRotationalEnergyModeforaDiatomicMolecule 100


    6.4 TheVibrationalEnergyModeforaDiatomicMolecule 104


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