Thermodynamics

241 Pages·2018·3.423 MB·English

by  Luscombe, James

Thermodynamics

Thermodynamics
James H. Luscombe
CRC Press
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Contents
Preface ix
SECTIONI ThermodynamicsBasics(forAdvancedStudents)
CHAPTER1(cid:4)Concepts of thermodynamics: Equilibrium, energy, and
irreversibility 3
1.1 THE MANY AND THE FEW 3
1.2 EQUILIBRIUM AND TIMELESSNESS 4
1.3 EXACT DIFFERENTIALS* 6
1.4 INTERNAL ENERGY: WORK, HEAT, AND BOUNDARIES 7
1.5 EMPIRICAL TEMPERATURE 11
1.6 EQUATION OF STATE FOR GASES 13
1.7 IRREVERSIBILITY: TIME REARS ITS HEAD 14
1.8 CONSTRAINTS AND STATE VARIABLES 16
1.9 THE MANY FACES OF WORK 17
1.10 CYCLIC RELATION* 18
1.11 RESPONSE FUNCTIONS 19
CHAPTER2(cid:4)Second law of thermodynamics: Direction of heat flow 25
2.1 THERMODYNAMICS OF CYCLES: SYSTEM AS A BLACK BOX 25
2.2 CLAUSIUS AND KELVIN STATEMENTS OF THE SECOND LAW 26
2.3 CARNOT THEOREM: UNIQUENESS OF ADIABATS 28
2.4 ABSOLUTE TEMPERATURE 29
CHAPTER3(cid:4)Entropy 33
3.1 CLAUSIUS INEQUALITY 33
3.2 THE BIRTH OF ENTROPY 34
3.3 ENTROPY, IRREVERSIBILITY, AND DISORGANIZATION 35
3.4 OPENING THE BLACK BOX: GIBBSIAN THERMODYNAMICS 38
3.5 CHEMICAL POTENTIAL AND OPEN SYSTEMS 39
3.6 HOMOGENEOUS FUNCTIONS* 39
v
vi (cid:4) Contents
3.7 EXTENSIVITY OF ENTROPY 40
3.8 GIBBS-DUHEM EQUATION 42
3.9 QUADRATIC FORMS* 43
3.10 STABILITY OF THE EQUILIBRIUM STATE: FLUCTUATIONS 43
3.11 DIRECTION OF FLOW IN THERMODYNAMIC PROCESSES 49
3.12 JACOBIAN DETERMINANTS* 49
CHAPTER4(cid:4)Thermodynamic potentials: The four ways to say energy 53
4.1 CRITERIA FOR EQUILIBRIUM 53
4.2 LEGENDRE TRANSFORMATION* 54
4.3 THE FOUR THERMODYNAMIC POTENTIALS 55
4.4 PHYSICAL INTERPRETATION OF THE POTENTIALS 56
4.5 MAXWELL RELATIONS 58
4.6 GIBBS ENERGY, CHEMICAL POTENTIAL, AND OTHER WORK 58
4.7 FREE ENERGY AND DISSIPATED ENERGY 59
4.8 HEAT DEATH OF THE UNIVERSE? 60
4.9 FREE EXPANSION AND THROTTLING 62
CHAPTER5(cid:4)Thermodynamics of radiation 67
5.1 KIRCHHOFF LAW OF THERMAL RADIATION 67
5.2 THERMODYNAMICS OF BLACK-BODY RADIATION 69
5.3 WIEN’S DISPLACEMENT LAW 73
5.4 COSMIC MICROWAVE BACKGROUND 79
CHAPTER6(cid:4)Phase and chemical equilibrium 81
6.1 LAGRANGE MULTIPLIERS* 81
6.2 PHASE COEXISTENCE 82
6.3 THERMODYNAMICS OF MIXTURES: IDEAL SOLUTIONS 87
6.4 LAW OF MASS ACTION 89
6.5 ELECTROCHEMICAL CELLS 90
6.6 GIBBS-HELMHOLTZ EQUATIONS 92
CHAPTER7(cid:4)Statistical entropy: From micro to macro 97
7.1 ENTROPY AND PROBABILITY 97
7.2 COMBINATORICS: LEARNING TO COUNT* 100
7.3 COARSE-GRAINED DESCRIPTIONS OF A CLASSICAL GAS 103
7.4 SACKUR-TETRODE EQUATION 108
Contents (cid:4) vii
7.5 VOLUME OF A HYPERSPHERE* 111
7.6 LEARNING TO COUNT WITH PHYSICS 111
7.7 GIBBS’S PARADOX, NOT 113
7.8 SUBTLETIES OF ENTROPY 115
CHAPTER8(cid:4)The third law: You can’t get to T = 0 121
8.1 ADIABATIC DEMAGNETIZATION 121
8.2 NERNST HEAT THEOREM 124
8.3 OTHER VERSIONS OF THE THIRD LAW 125
8.4 CONSEQUENCES OF THE THIRD LAW 127
8.5 UNATTAINABILITY OF ABSOLUTE ZERO TEMPERATURE 127
8.6 RESIDUAL ENTROPY OF ICE 129
CHAPTER9(cid:4)To this point 135
SECTIONII AdditionalTopicsinThermodynamics
CHAPTER10(cid:4)Carathe´odory formulation of the second law 149
10.1 INTEGRABILITY CONDITIONS AND THERMODYNAMICS 149
10.2 CARATHE´ODORY THEOREM 157
10.3 CARATHE´ODORY’S PRINCIPLE AND THE SECOND LAW 158
CHAPTER11(cid:4)Negative absolute temperature 163
11.1 IS NEGATIVE ABSOLUTE TEMPERATURE POSSIBLE? 163
11.2 NEGATIVE ABSOLUTE IS HOTTER THAN POSITIVE ABSOLUTE 166
11.3 NEGATIVE-TEMPERATURE THERMODYNAMICS 167
CHAPTER12(cid:4)Thermodynamics of information 171
12.1 ENTROPY AS MISSING INFORMATION 171
12.2 MAXWELL’S DEMON: A WAY TO BEAT THE SECOND LAW? 172
12.3 DEMISE OF THE DEMON: FLUCTUATIONS AND INFORMATION 174
12.4 IS ENTROPY INFORMATION? 178
12.5 INFORMATION IS PHYSICAL 183
CHAPTER13(cid:4)Black hole thermodynamics 187
13.1 BLACK HOLES AND THERMODYNAMICS 187
viii (cid:4) Contents
13.2 HAWKING RADIATION 189
13.3 ENTROPY AND MISSING INFORMATION 190
13.4 LAWS OF BLACK HOLE THERMODYNAMICS 192
13.5 IS GRAVITY THERMODYNAMICS? 193
CHAPTER14(cid:4)Non-equilibrium thermodynamics 195
14.1 NON-EQUILIBRIUM PROCESSES 196
14.2 ONSAGER THEORY 197
14.3 ENTROPY BALANCE EQUATION 199
14.4 ENTROPY FLOW AND ENTROPY CREATION 205
14.5 THERMOELECTRICITY 206
CHAPTER15(cid:4)Superconductors and superfluids 209
15.1 LONDON THEORY 209
15.2 ROTATING SUPERCONDUCTOR, LONDON MOMENT 212
15.3 TWO-FLUID MODEL 213
15.4 FOUNTAIN EFFECT 215
Epilogue: Where to now? 217
Bibliography 219
Index 225
Preface
Thepeculiarmultiplicityofformulationandreformulationofthebasicthermodynamic
formalismisresponsiblefortheapparentcomplexityofasubjectthatinitsnakedform
isquitesimple.—H.B.Callen[1,p85]
THERMODYNAMICS and statistical mechanics are core components of physics curricula. Sta-
tistical mechanics, together with quantum mechanics, provides a framework for relating the
macroscopic properties of large collections of atoms (such as in a solid) to the microscopic prop-
erties of their constituents. The term macroscopic is difficult to define because samples of matter
barelydiscernibletohumansensescontainenormousnumbersofatoms.Statisticalmechanicsuses
probabilitytomakepredictionsinthefaceofincompleteinformation.Predictionsaretheoretically
possiblewhenthestateofeveryatominasystemisknown.Thetroubleis,suchinformationisnot
availablefortheenormousnumberofatomscomprisingmacroscopicsystems,andwemustresort
toprobabilisticmethods.Historically,statisticalmechanicswasdevelopedtoaccountfortheresults
ofthermodynamics,aphenomenologicaltheorythatpresupposesnoknowledgeofthemicroscopic
components of matter, and instead makes use of concepts such as temperature and entropy. The
relationbetweenthetwosubjectsexemplifiesacommonthemeinphysics:Theroleofmicroscopic
theoryistoexplaintheresultsofmacroscopictheory.
In years past, thermodynamics and statistical mechanics were taught separately. With the in-
variablecompressionofcurricula(squeezemorecontentintotime-constrainedcurricula),therehas
been a movement to combine the subjects under the rubric of thermal physics. Students can find
themselvesonshakygroundwhenthermodynamicideasareintroducedasanoutgrowthofthesta-
tisticalapproach,becausethey’renotfamiliarwiththermodynamics.Thermodynamicsisadifficult
subject that takes time to learn. It’s difficult because of its generality. The application of general
theories to specific instances taxes a student’s understanding of the entire theory; it takes time to
becomeproficientinthermodynamics,tolearnitsscopeandmethods.
Ihaveundertakento writearelativelybrief,yetin-depth review ofthermodynamics,apre´cis,
with emphasis on the structure of the theory. The heart of thermodynamics is entropy—students
mustlearnfromtheoutsetthatthermodynamicsmainlyisaboutentropy.1 Tothatend,Chapter1,
Concepts of Thermodynamics, has been written with the goal of introducing everything that can
besaidusingonlythefirstlawofthermodynamics.Therestofthebookthereforeisaboutentropy
insomewayorform.Entropy,whichwasdiscoveredintheanalysisofsteamengines,pertainsto
allformsofmatter(solid,liquid,gas)butalsotosuchdisparatesystemsasinformationandblack
holes:Entropyisauniversalfeatureofthephysicalworld.Likeanythinggenuinelynew,itcannotbe
reducedtoconceptsgainedthroughpriorexperience.Entropyinmyopinionshouldbelearnedfirst
fromthephenomenologicalperspective.Whenlaterit’sstatedthatthestatisticaltheoryofentropy
isinaccordwiththeresultsofthermodynamics,consistencyrequiresthatthelatterstandinitsown
right.Whilethermodynamicsisfirmlyrootedinclassicalphysics,thereareanumberofinstances
wherethermodynamicsuncannilyanticipatestheexistenceofquantummechanics(notedthrough-
outthebook).Thisbookisofferedagainstthebackdropofthecorpusofphysicaltheorytowhich
thestudentisunabashedlyassumedtohavebeenexposed.Thereareworksonthermodynamicsthat
1Maxwellwrote,“Thetouchstoneofatreatiseonthermodynamicsiswhatiscalledthesecondlaw.”[2,p667]
ix