The Principles of Thermodynamics

344 Pages·2013·6.84 MB·English

by  N.D. Hari Dass

The Principles of
Thermodynamics
T
hermodynamics
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Unshaken by the revolutionary developments of quantum theory, the
foundations of thermodynamics have demonstrated great resilience. The hT
impact of thermodynamics on scientific thought as well as its practical eh
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impact have been unmatched by any other field of science. Its applications r
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range over physics, chemistry, physical chemistry, engineering, and, more
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recently, biology and even black holes. The Principles of Thermodynamics oin
offers a fresh perspective on classical thermodynamics, highlighting its dc
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elegance, power, and conceptual economy. The book demonstrates how yp
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much of natural phenomena can be understood through thermodynamics. ne
s
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In a single volume, the author distills the essence of classic texts to give o
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a balanced, in-depth treatment of the important conceptual and technical
developments in thermodynamics. He presents the history of ideas and i
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explains how thermodynamics evolved a few basic “laws” that have been
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incredibly successful, despite being developed without knowledge about
the atomic structure of matter or the laws governing the behavior of atoms.
The resilience of thermodynamic principles is illustrated by the tremendous
range of applications, from osmotic pressure and how solids melt and
liquids boil, all the way to the incredible race to reach absolute zero, and to
the modern theme of the renormalization group.
Drawing on his extensive teaching and research experience, the author
approaches the topics from different angles using a variety of techniques,
which helps readers to see how thermodynamics can be applied to many
situations, and in many ways. He also includes a large number of solved
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examples and problems in each chapter, as well as a carefully selected a
r
guide to further reading. Emphasizing the importance of thermodynamics i
D
in contemporary science and engineering, this book combines fundamental a
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principles and applications to offer an integrated resource for students,
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teachers, and experts alike.
K14872
N. D. Hari Dass
K14872_Cover.indd 1 7/23/13 2:01 PM
The Principles of
T
hermodynamics

The Principles of
T
hermodynamics
N. D. Hari Dass
CRC Press
Taylor & Francis Group
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Version Date: 20130827
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Dedication
.
IdedicatethisbooktomybelovedhighschoolteacherSri.H.AnanthaRao(1907-
2011),wholivedtruetothespiritofscience.Heopenedourmindstothewonderful
worldofphysics.Tillhislastdayshewaspreoccupiedwithscience,andinparticular
whethermodernsciencewasaddressingtherightquestions.
I also dedicate this book to my parents. To my mother, Venkatalakshmi, who,
despite gnawing poverty, made the education of her children her prime objective
inlife.Andtomyfather,Desikachar,who,despitebeingveryorthodoxreligiously
neverhinderedourchoicesinlife.

Contents
Preface.....................................................................................................................xiii
Guideforreadersandteachers.................................................................................xv
Chapter1 TheBeginnings.....................................................................................1
1.1 Temperatureandthermometry..................................................2
1.1.1 Uniformtemperaturescale...........................................3
1.1.2 Non-uniformtemperaturescales..................................4
1.1.3 Materialsforthermometry...........................................5
1.2 Idealgaslaws............................................................................7
1.2.1 TheKelvinscale..........................................................9
1.2.2 Non-idealgases..........................................................11
1.3 Heatandspecificheats............................................................11
1.3.1 Natureofheat.............................................................12
1.3.2 Statesandtransformations.........................................13
1.3.3 Someexamples..........................................................15
1.4 SadiCarnotandthemotivepowerofheat..............................17
1.4.1 Infinitesimalandfinitecycles....................................26
1.5 SteamenginesandtheClapeyronEquation...........................28
1.6 Problems.................................................................................32
Chapter2 FirstLaw—TheE=Mc2ofThermodynamics.................................33
2.1 Thefallofthecaloric..............................................................33
2.2 Thepathtothefirstlaw..........................................................34
2.3 Thefirstlawofthermodynamics............................................37
2.4 Someapplicationsofthefirstlaw...........................................40
2.4.1 Internalenergyofidealgases....................................41
2.4.2 Isochoricchanges.......................................................41
2.4.3 Isobaricchanges.........................................................41
2.4.4 Adiabaticchangesinanidealgas..............................42
2.4.5 Isothermalchanges....................................................43
2.4.6 Heatsoftransformation..............................................43
2.4.7 Enthalpy.....................................................................43
2.5 Problems.................................................................................48
2.6 Suggestedreadingforthisbookingeneral.............................49
vii
viii Contents
Chapter3 TheSecondandThirdLaws...............................................................51
3.1 Perpetuummobiles.................................................................52
3.1.1 Perpetualmachinesofthefirstkind...........................52
3.1.2 Perpetualmachinesofthesecondkind......................53
3.2 Theentropyaxiom:thefirstpartofsecondlaw.....................53
3.2.1 Abonanzafromfirstlawforidealgases...................53
3.2.2 Aconsequenceoftheentropyaxiom.........................54
3.3 EntropyaxiomanduniversalityofCarnotcycles...................55
3.3.1 IdealgasCarnotcycle................................................59
3.3.2 CompositionofCarnotcycles....................................60
3.4 Historicalformulationsofsecondlaw....................................61
3.4.1 ConsequencesofClausiusInequality........................63
3.5 Secondlawandirreversibility................................................65
3.5.1 Secondlawandarrowoftime....................................69
3.5.2 Entropyanddisorder..................................................70
3.5.3 Entropyandinformation............................................70
3.6 Anabsolutescaleoftemperature............................................70
3.7 Applicationsofthefirstandsecondlaws...............................72
3.8 Thirdlawofthermodynamics-theNernst-Planck
postulate..................................................................................79
3.9 Problems.................................................................................85
Chapter4 CarnotCycles-TheTuringMachinesofThermodynamics..............87
4.1 ThegasCarnotcycles.............................................................87
4.1.1 Theidealgascycles...................................................87
4.1.2 ThevanderWaalscycle............................................88
4.2 ThesteamCarnotcycle..........................................................89
4.3 TheStirlingengine.................................................................90
4.4 TheOttocycle.........................................................................92
4.4.1 TheDieselcycle.........................................................93
4.5 TheBraytoncycle...................................................................93
4.5.1 ThemagneticBraytoncycle......................................94
4.6 Carnotcyclewithphotons......................................................96
4.6.1 TheThermodynamicsoftheradiationfield...............96
4.6.2 PhotonCarnotcycle...................................................99
4.6.3 Thethermodynamicgatewaytoquantumworld......100
4.7 Problems...............................................................................101
Chapter5 SpecificHeats:MagnificentBridges ...............................................103
5.1 Abriefhistory.......................................................................103
5.2 Varietiesofspecificheats......................................................105
5.2.1 Negativespecificheats.............................................106
5.3 Specificheatsandthethirdlaw............................................107
Contents ix
5.3.1 Specificheatsandcoolingpowers...........................107
5.4 Specificheatsandmicroscopics...........................................108
5.5 Specificheatsheraldquantumtheory!..................................109
5.5.1 Einsteinandspecificheats.......................................109
5.5.2 DebyeTheory...........................................................112
5.5.3 Specificheatsofquantumidealgases......................113
5.6 Problems...............................................................................116
Chapter6 StructureofThermodynamicTheories............................................119
6.1 Extensiveandintensivevariables:general...........................122
6.2 TheFundamentalEquations.................................................124
6.2.1 Intensivevariablesandthefundamentalequation...125
6.2.2 TheEulerrelations...................................................126
6.2.3 TheGibbs-Duhemrelations.....................................127
6.3 Trueequationsofstate..........................................................127
6.4 Multicomponentsystems......................................................128
6.5 EntropyofmixingandtheGibbsparadox...........................130
6.5.1 Extensivityrevisited.................................................132
6.6 Workedoutexamples............................................................133
6.6.1 Fundamentalequationsandequationsofstate.........133
6.6.2 Gibbs-Duhemrelations............................................135
6.7 Axiomaticintensivevariablesandequilibrium....................135
6.7.1 Stabilityofequilibrium............................................136
6.8 Problems...............................................................................137
Chapter7 ThermodynamicPotentialsandMaxwellRelations.........................139
7.1 Thermodynamicpotentials...................................................139
7.1.1 Internalenergyandenthalpy....................................140
7.1.2 Helmholtzfreeenergy..............................................140
7.1.3 Gibbsfreeenergy.....................................................142
7.2 Maxwell’srelations...............................................................143
7.2.1 Howmanydifferentpotentials?...............................145
7.2.2 Inclusionofchemicalpotential................................146
7.3 Problems...............................................................................147
Chapter8 MagneticSystems............................................................................149
8.1 Introduction...........................................................................149
8.2 Thermodynamicpotentials...................................................162
8.2.1 InclusionofPdVandμdntermsindU....................163
8.2.2 MagneticEulerrelations..........................................163
8.2.3 Countingthemagneticpotentials.............................164
8.2.4 EstimatingPdVvsB dM .......................................165
e
8.2.5 Equationofstateformagneticsystems...................166