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Thermodynamics A complete undergraduate course
Andrew M. Steane
OXFORD \JNIVERSITY PRESS
Contents
How to use this book (t)
1.1 For the student 1.2 For the teacher
2 Introducing thermodynamics 3
3 A survey of thermodynamic ideas 7
3.1 Energy and entropy 7
3.2 Concepts and terminology 12 3.2.1 System 12 3.2.2 State 14 3.2.3 Extensive, intensive 18 3.2.4 Thermodynamic equilibrium 20 3.2.5 Temperature 22 3.2.6 Quasistatic 22 3.2.7 Reversible and irreversible 23 3.2.8 Adiathermal, isentropic, adiabatic, isothermal 25 3.2.9 Expansion coefficients, heat capacities 26 3.2.10 Thermal reservoir 29
3.3 The laws of thermodynamics 29
3.4 Where we are heading 32
Exercises 33
4 Some general knowledge 34
4.1 Density, heat capacity 34
4.2 Moles 35
4.3 Boltzmann constant, gas constant 36
4.4 Pressure and STP 37
4.5 Latentheat 37 4.6 Magnetic properties 38
s Mathem atical tools 40
5.1 Working with partial derivatives 40 5.1.1 Reciprocal and reciprocity theorems 42 5.1.2 lntegrating 45 5.1.3 Mixed derivatives 46
tsections rnarked with a dagger below are optional reading. They can be omitted without the loss of inf orrnation required later in the book.
vili Cont.ents
5 .2 Proper and improper differentials, function of state 5.2.1 Integrating factor
5.3 Some further observations 5.3.1 Alternative derivation of reciprocal and reciprocity theorems 5.3.2 Integration in general
Exercises
6 Zeroth law, equation of state
6.1 Empirical temperature 6.1.1 Equation of state 6.1.2 Algebraic argument (t)
6.2 Some example equations of state 6.2.1 Ideal gas 6.2.2 Thermal radiation 6.2.3 Solids and wires 6.2.4 Paramagnetic material 6.2.5 Equations of state for other properties
6.3 Thermometry
Exercises
7 First law, internal energy
7 .1 Defining internal energy 7 .1.1 Heat and work
7 .2 Work by compression
7 .3 Heat capacities 7.3.1 Energy equation 7.3.2 Relation of compressibilities
and heat capacities
7 .4 Solving thermodynamic problems
7.5 Expansion 7.5.1 Free expansion ofideal gas 7.5 .2 Adiabatic expansion of ideal gas 7.5.3 Adiabatic atmosphere 7.5.4 Fast and yet adiabatic?
Exercises
8 The second law and entropy
8.1 Heat engines and the Carnot cycle 8.1.1 Heat pumps and refrigerators 8.1.2 1\vo impossible things (equivalence ofKelvin and Clausius Statements)
8.2 Carnot's theorem and absolute temperature 8.2.1 Carnot's theorem: reversible engines are equally, and the most, efficient 8.2.2 Existence of an absolute temperature measure 8.2.3 Hot heat is more valuable than cold heat
46 49
49 49 50 51
52
54 55 57
59 59 61 62 63 65
66
68
70
70 73 74 77 80
82
83
85 85 86 87 88 89
93
93 95 96 97 97 98
101
8.3 Clausius' theorem and entropy
8.4 Tue first and second laws together
8.5 Summary
Exercises
9 Understanding entropy
9.1 Examples 9.1.1 Entropy content 9.1.2 Enttopy production and enttopy flow
9.2 But what is it? 9.2.1 Entropy increase in a free expansion
9.3 Gibbs' paradox 9.3.1 Entropy ofmixing 9.3.2 Reversible mixing
9.4 Specific heat anomalies
9.5 Maxwell's daemon 9.5.1 Szilard engine 9.5.2 The Feynman-Smoluchowski ratchet
9.6 The principle of detailed balance
9. 7 Adiabatic surfaces et) 9.8 Irreversibility in the universe
Exercises
10 Heat ftow and thermal relaxation
10.1 Thermal conduction; diffusion equation 10.1.l Steady state 10.1.2 Time-dependent
10.2 Relaxation time
10.3 Speed of sound (t) 10.3.1 Ultra-relativistic gas
Exercises
11 Practical heat engines
11 .1 Tue maximum work theorem 11.1.1 lmperfections
11.2 Otto cycle
Exercises
12 Introducing chemical potential
12.1 Chemical potential of an ideal gas 12.1.1 Example: the isothermal atmosphere
12.2 Saha equation (t)
Exercises
Contents ix
102 105
106
106
108
109 111 112
113 115 116 118 119 120
122 123 125
127
128
131
133
136
136 138 139
145
146 148
148
150
152 152
153
155
157
161 163
165
167
x Contents
13 Functions and methods
13.1 The fundamental relation 13.1.1 Euler relation, Gibbs-Duhem relation
13.2 Thermodynamic potentials 13.2.1 Free energy as a form of potential energy 13.2.2 Natural variables and thermodynamic potentials 13.2.3 Maxwell relations 13.2.4 Obtaining one potential function from another
13.3 Basic results for closed systems 13.3.1 Relating intemal energy to equation of state 13.3.2 Sackur-Tetrode equation 13.3.3 Complete thermodynamic information
Exercises
14 Elastic bands, rods, bubbles, magnets
14.1 Expressions for work 14.2 Rods, wires, elastic bands 14.3 Surface tension 14.4 Paramagnetism
14.4.1 Idealparamagnet 14.4.2 Cooling by adiabatic demagnetization
14.5 Electric and magnetic work (t) 14.5.1 Dielectrics and polarization 14.5.2 Magnetic work
14.6 lntroduction to the partition function (t) Exercises
15 Modelling real gases
15 .1 van der Waals gas 15.1.1 Phase change 15.1.2 Critical parameters and the law of corresponding states
15.2 Redlich-Kwong, Dieterici, and Peng-Robinson gas Exercises
16 Expansion and flow processes
16.1 Expansion coefficients 16.2 U: free expansion
16.2.1 Deriving the equation of state of an ideal gas
16.3 H: throttle process: Joule-Kelvin expansion 16.3 .1 Bernoulli equation 16.3.2 Cooling and liquification of gases
16.4 Generalflow process 16.4.1 S and H: the gas turbine
Exercises
169
169 170 172 174 175 176 177
177 178 182 186 186
188
188 188 190 192 195 197 200 202 207 210 212
216
219 220 222 224 226
228
228 229 229
230 231 232 236 237 239
17 Stability and free energy
17 .1 Isolated system: maximum entropy 17 .1.1 Equilibrium condition with intemal restrictions 17 .1.2 Tue minimum energy principle 1 7 .1.3 Stability
17.2 Phase change
17.3 Free energy and availability 17 .3.1 Free energy and equilibrium
Exercises
18 Reinventing the subject
18.1 Some basic derivations from maximum entropy
18.2 Caratheodory formulation ofthe second law (t) 18.3 Negative temperature (t)
19 Thermal radiation
19.1 Some general observations about thermal radiation 19 .1.1 Black body radiation: a first look
19.2 Basic thermodynamic arguments 19.2.1 Equation of state and Stefan-Boltzmann law 19.2.2 Comparison with ideal gas 19.2.3 Adiabatic expansion and Wien's laws (t)
19.3 Cosmic microwave background radiation Exercises
20 Radiative heat transfer
20.1 Tue greenhouse effect
Exercises
21 Chemical reactions
21.1 Basic considerations 21.1.1 Reaction rate
21.2 Chemical equilibrium and the law of mass action 21.2 .1 Van 't Hoff equation 21.2.2 Chemical terminology
21.3 Tue reversible electric cell (t)
Exercises
22 Phase change
22.1 General introduction 22.1.1 Phase diagram 22.1.2 Some interesting phase diagrams
22.2 Basic properties offirst-order phase transitions 22.3 Clausius-Clapeyron equation
Contents xi
243
243 245 246 247
249
250 253 257
259
262
263 265
268
268 274
275 279 282 283
288 289
291
294
297
299
299 301 301 305 306 307
309
311
311 312 314
317 320
xii Contents
22.3.1 Vapour-liquid and liquid-solid coexistence lines 22.3.2 Gibbs phase rule 22.3.3 Behaviour of the chemical potential
22.4 The type-! superconducting transition (t) Exercises
23 The third law
23.1 Response functions 23.2 Unattainability theorem
23.3 Phase change 23.4 Absolute entropy and chemical potential
24 Phase change, nucleation, and solutes
24.1 Treatment of surface effects
24.2 Metastable phases 24.2.1 Nucleation
24.3 Colligative properties 24.3.1 Osmotic pressure 24.3.2 lnftuence of dissolved particles on phase transitions
24.4 Chapter summary
Exercises
25 Continuous phase transitions
25.1 Orderparameter 25.2 Critical exponents 25.3 Landau mean field theory
25.3.1 Application to ferromagnetism 25.4 Binary mixtures Exercises
26 Self-gravitation and negative heat capacity
26.1 Negative heat capacity 26.1.1 Jeans length
26.2 Black holes and Hawking radiation Exercises
27 Fluctuations
27 .1 Probability of a departure from the maximum entropy point 27.1.1 Is there a violation of the second law?
27.2 Calculating the ftuctuations 27.2.1 More general constraints 27 .2.2 Some general observations
27 .3 Interna! ftows
27.4 Fluctuation as a function oftime
323 325 326 326 329
331
332 333
334 335
336
336 338 341
347 347 350 353 353
355
357 359 361 366 370 373
375
375 377 378 381
382
383 384
385 387 391 393
395
27.5 Johnson noise Exercises
28 Thermoelectricity and entropy flow
28.1 Thermoelectric effects 28.1.1 Thomson's treatment
28.2 Entropy gradients and Onsager's reciprocal relations 28.2.1 Derivation of Onsager's reciprocal relation 28.2.2 Application 28.2.3 Entropy current, entropy production rate
Exercises
Appendix A Electric and magnetic work
Appendix B More on natural variables and free energy
Appendix C Some mathematical results
Bibliography
Index
Conunts xili
398 401
403
403 406
409 411 416 41 7 418
421
424
428
431
433
