A Concise Introduction to Thermodynamics for Physicists

237 Pages·2022·10.633 MB·English

by  Patricia Faisca

A Concise Introduction
to Thermodynamics for
Physicists
This introductory textbook provides a synthetic overview of the laws and formal aspects of
thermodynamics and was designed for undergraduate students in physics, and in the physical
sciences. Language and notation have been kept as simple as possible throughout the text.
While this is a self-contained text on thermodynamics (i.e., focused on macroscopic physics),
emphasis is placed on the microscopic underlying model to facilitate the understanding of key
concepts such as entropy, and motivate a future course on statistical physics.
This book will equip the reader with an understanding of the scope of this discipline and of its
applications to a variety of physical systems.
Throughout the text readers are continuously challenged with conceptual questions that
prompt reflection and facilitate the understanding of subtle issues. Each chapter ends by pre-
senting worked problems to support and motivate self-study, in addition to a series of proposed
exercises whose solutions are available as supplementary material.
Features
• Pedagogically designed, including illustrations, keyword definitions, highlights, summaries
of key ideas and concepts, and boxes with additional topics that complement the materials
presented in the main text.
• Presents active reading strategies, such as conceptual problems, discussion questions,
worked examples with comments, end of chapter problems, and further reading to stimu-
late engagement with the text.
• Guides the reader with ease through a difficult subject by providing extra help whenever
needed to overcome the more demanding technical and conceptual aspects.
Patrícia Faísca is Assistant Professor (with habilitation) in the Department of Physics, Faculty
of Sciences, at the University of Lisbon, and principal investigator at the Biosystems and Integra-
tive Sciences Institute. She received a PhD in Physics in 2002 from the University of Warwick as
part of the Gulbenkian PhD Program in Biology and Medicine. She has a broad interdisciplinary
education covering Physics, Biology and Mathematics. Her fields of interest include biological
physics, thermodynamics, and statistical physics.

A Concise Introduction
to Thermodynamics for
Physicists
Patrícia Faísca
First edition published 2023
by CRC Press
6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742
and by CRC Press
4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
CRC Press is an imprint of Taylor & Francis Group, LLC
© 2023 Patrícia F.N. Faísca
Reasonable efforts have been made to publish reliable data and information, but the author and pub-
lisher cannot assume responsibility for the validity of all materials or the consequences of their use.
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ISBN: 978-0-367-55084-4 (hbk)
ISBN: 978-0-367-54641-0 (pbk)
ISBN: 978-1-003-09192-9 (ebk)
DOI: 10.1201/9781003091929
Publisher’s note: This book has been prepared from camera-ready copy provided by the authors.
Typeset in Nimbus Roman
by KnowledgeWorks Global Ltd.
Dedication
Tothose
wholedmeintoScience

Contents
Preface.......................................................................................................................xi
Contributors............................................................................................................xiii
SECTION I The Laws of Thermodynamics
Chapter1 ThermodynamicsKeyConcepts......................................................3
1.1 Introduction.............................................................................3
1.2 Thermodynamicequilibrium..................................................4
1.3 Thermodynamicsystem..........................................................6
1.4 Theidealgas...........................................................................8
1.5 Internalenergy......................................................................10
1.6 Extensiveandintensiveproperties........................................12
1.7 Thermodynamicprocesses....................................................13
1.8 Constraintsandprocesses.....................................................15
1.9 Heatandheatcapacity..........................................................16
1.10 Thezerothlawofthermodynamics......................................18
1.11 Abriefintroductiontothekinetictheoryofgases...............20
1.11.1 Velocityspace..........................................................20
1.11.2 Velocitydistribution.................................................22
1.11.3 Derivingthepressureequationofstate....................27
1.12 Learningoutcomes................................................................29
1.13 Workedproblems..................................................................30
1.14 Suggestedproblems..............................................................32
Chapter2 TheFirstLaw................................................................................37
2.1 Introduction...........................................................................37
2.2 Thermodynamicwork...........................................................37
2.3 Thefirstlawofthermodynamics..........................................40
2.4 Exactdifferentialsandstatefunctions..................................41
2.5 Rewritingthefirstlaw...........................................................43
2.6 JouleExperiment..................................................................43
2.7 Usingthefirstlaw.................................................................45
2.7.1 Heatcapacityatconstantvolume............................45
2.7.2 Heatcapacityatconstantpressure...........................46
2.7.3 Isothermal compression and expansion of the
idealgas...................................................................48
vii
viii Contents
2.7.4 Adiabatic compression and expansion of the
idealgas...................................................................49
2.7.5 Thermodynamiccycles............................................51
2.8 Learningoutcomes................................................................51
2.9 Workedproblems..................................................................51
2.10 Suggestedproblems..............................................................54
Chapter3 TheSecondLaw............................................................................59
3.1 Introduction...........................................................................59
3.2 TheCarnotengine.................................................................60
3.3 TheinvertedCarnotcycle.....................................................63
3.4 Thesecondlawofthermodynamics.....................................65
3.5 Carnottheorem.....................................................................68
3.6 Entropychangeinreversibleprocesses................................69
3.7 Thefundamentalconstraint..................................................72
3.8 Clausiustheorem..................................................................75
3.9 Analysisofirreversibleprocesses.........................................79
3.9.1 Jouleexpansion........................................................79
3.9.2 Systemsinthermalcontact......................................80
3.9.3 Mixingtwoidealgases............................................81
3.10 Thestatisticalmeaningofentropy........................................82
3.11 Entropyanddisorder.............................................................85
3.12 Learningoutcomes................................................................86
3.13 Workedproblems..................................................................86
3.14 Suggestedproblems..............................................................91
Chapter4 TheThirdLaw...............................................................................95
4.1 Introduction...........................................................................95
4.2 Nernsttheorem......................................................................95
4.3 Maximumcooling.................................................................96
4.4 Nernstunattainabilityprinciple............................................97
4.5 Logical equivalence between Nernst theorem and the
unattainabilityprinciple........................................................97
4.6 Openquestions......................................................................98
4.7 Theidealgasnearabsolutezero...........................................98
4.8 Learningoutcomes................................................................99
SECTION II The Structure of Thermodynamics
Chapter5 ThermodynamicPotentials..........................................................103
5.1 Introduction.........................................................................103
5.2 Enthalpy..............................................................................105
5.3 Freeenergy.........................................................................109
Contents ix
5.3.1 Helmholtzfreeenergy............................................109
5.3.2 Gibbsfreeenergy...................................................111
5.4 Maxwellrelations...............................................................115
5.5 Thermodynamiccoefficients...............................................116
5.6 Opensystemsandchemicalpotential.................................118
5.7 Multicomponentsystems....................................................121
5.8 Thegrandpotential.............................................................122
5.9 Massieufunctions...............................................................123
5.10 Thermodynamicequilibriumrevisited................................124
5.11 Stabilityofequilibriumstates.............................................127
5.11.1 Stabilityandthesignofthermodynamic
coefficients.............................................................130
5.11.2 Metastabilityofequilibriumstates.........................132
5.12 Learningoutcomes..............................................................134
5.13 Workedproblems................................................................134
5.14 Suggestedproblems............................................................137
Chapter6 ThermodynamicsofExtensiveSystems......................................141
6.1 TheEulerequation..............................................................141
6.2 TheGibbs-Duhemequationandthermodynamic
degreesoffreedom.............................................................143
6.3 ApplyingtheGibbs-Duhemequation.................................145
6.4 Molarquantities..................................................................147
6.5 Partialmolarquantities.......................................................148
6.6 Learningoutcomes..............................................................150
6.7 Workedproblems................................................................150
6.8 Suggestedproblems............................................................152
SECTION III Applications
Chapter7 PhaseTransitions.........................................................................155
7.1 Introduction.........................................................................155
7.2 Phase...................................................................................156
7.3 TheGibbsphaserule..........................................................156
7.4 Phasediagrams...................................................................158
7.5 Phasetransitions.................................................................159
7.6 Clausius-Clapeyronequationandlatentheat.....................163
7.7 ThevanderWaalsgasmodel.............................................165
7.7.1 Maxwellconstruction.............................................168
7.7.2 Criticalisothermandcorrespondingstates............169
7.8 Guggenheimcurveandcriticality.......................................171
7.9 Criticalexponents...............................................................172
7.10 Learningoutcomes..............................................................174