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BK

Second edition

Oxford ; Oxford University Press, 2010

xviii, 493 stran : ilustrace ; 25 cm

ISBN 978-0-19-956210-7 (brožováno)

Obsahuje bibliografii na stranách 485-487 a rejstřík

001636151

Contents // Preface vii // Preface to the second edition x // I Preliminaries 1 // 1 Introduction 2 // 1.1 What is a mole? 3 // 1.2 The thermodynamic limit 4 // 1.3 The ideal gas 6 // 1.4 Combinatorial problems 7 // 1.5 Plan of the book 9 // Exercises 12 // 2 Heat 13 // 2.1 A definition of heat 13 // 2.2 Heat capacity 14 // Exercises 17 // 3 Probability 18 // 3.1 Discrete probability distributions 19 // 3.2 Continuous probability distributions 20 // 3.3 Linear transformation 21 // 3.4 Variance 22 // 3.5 Linear transformation and the variance 23 // 3.6 Independent variables 24 // 3.7 Binomial distribution 26 // Further reading 29 // Exercises 29 // 4 Temperature and the Boltzmann factor 32 // 4.1 Thermal equilibrium 32 // 4.2 Thermometers 33 // 4.3 The microstates and macrostates 35 // 4.4 A statistical definition of temperature 36 // 4.5 Ensembles 38 // 4.6 Canonical ensemble 38 // 4.7 Applications of the Boltzmann distribution 42 // Further reading 46 // Exercises 46 // II Kinetic theory of gases // 47 // 5 The Maxwell—Boltzmann distribution 48 // 5.1 The velocity distribution 48 // 5.2 The speed distribution 49 // 5.3 Experimental justification 51 // Exercises 54 // 6 Pressure 56 // 6.1 Molecular distributions 57 // 6.2 The ideal gas law 58 // 6.3 Dalton’s law 60 // Exercises 61 // 7 Molecular effusion 64 // 7.1 Flux 64 // 7.2 Effusion 66 // Exercises 69 // 8 The mean free path and collisions 70 // 8.1 The mean collision time 70 // 8.2 The collision cross-section 71 // 8.3

The mean free path 73 // Exercises 74 // III Transport and thermal diffusion 75 // 9 Transport properties in gases 76 // 9.1 Viscosity 76 // 9.2 Thermal conductivity 81 // 9.3 Diffusion 83 // 9.4 More detailed theory 86 // Further reading 88 // Exercises 89 // 10 The thermal diffusion equation 90 // 10.1 Derivation of the thermal diffusion equation 90 // 10.2 The one-dimensional thermal diffusion equation 91 // 10.3 The steady state 94 // 10.4 The thermal diffusion equation for a sphere 94 // 10.5 Newton’s law of cooling 99 // 10.6 The Prandtl number 100 // 10.7 Sources of heat 101 // 10.8 Particle diffusion 102 // Exercises 103 // IV The first law 107 // 11 Energy 108 // 11.1 Some definitions 108 // 11.2 The first law of thermodynamics 110 // 11.3 Heat capacity 112 // Exercises 115 // 12 Isothermal and adiabatic processes 118 // 12.1 Reversibility 118 // 12.2 Isothermal expansion of an ideal gas 120 // 12.3 Adiabatic expansion of an ideal gas 121 // 12.4 Adiabatic atmosphere 121 // Exercises 123 // V The second law 125 // 13 Heat engines and the second law 126 // 13.1 The second law of thermodynamics 126 // 13.2 The Carnot engine 127 // 13.3 Carnot’s theorem 130 // 13.4 Equivalence of Clausius’ and Kelvin’s statements 131 // 13.5 Examples of heat engines 131 // 13.6 Heat engines running backwards 133 // 13.7 Clausius’ theorem 134 // Further reading 137 // Exercises 137 // 14 Entropy 140 // 14.1 Definition of entropy 140 // 14.2 Irreversible change 140 // 14.3 The first

law revisited 142 // 14.4 The Joule expansion 144 // 14.5 The statistical basis for entropy 146 // 14.6 The entropy of mixing 147 // 14.7 Maxwell’s demon 149 // 14.8 Entropy and probability 150 // Exercises 153 // 15 Information theory 157 // 15.1 Information and Shannon entropy 157 // 15.2 Information and thermodynamics 159 // 15.3 Data compression 160 // 15.4 Quantum information 162 // 15.5 Conditional and joint probabilities 165 // 15.6 Bayes’ theorem 165 // Further reading 168 // Exercises 169 // VI Thermodynamics in action 171 // 16 Thermodynamic potentials 172 // 16.1 Internal energy, U 172 // 16.2 Enthalpy, H 173 // 16.3 Helmholtz function, F 174 // 16.4 Gibbs function, G 175 // 16.5 Constraints 176 // 16.6 Maxwell’s relations 179 // Exercises 187 // 17 Rods, bubbles, and magnets 191 // 17.1 Elastic rod 191 // 17.2 Surface tension 194 // 17.3 Electric and magnetic dipoles 195 // 17.4 Paramagnetism 196 // Exercises 201 // 18 The third law 203 // 18.1 Different statements of the third law 203 // 18.2 Consequences of the third law 205 // Exercises 208 // VII Statistical mechanics 209 // 19 Equipartition of energy 210 // 19.1 Equipartition theorem 210 // 19.2 Applications 213 // 19.3 Assumptions made 215 // 19.4 Brownian motion 217 // Exercises 218 // 20 The partition function 219 // 20.1 Writing down the partition function 220 // 20.2 Obtaining the functions of state 221 // 20.3 The big idea 228 // 20.4 Combining partition functions 228 // Exercises 232 // 21 Statistical

mechanics of an ideal gas 233 // 21.1 Density of states 233 // 21.2 Quantum concentration 235 // 21.3 Distinguishability 236 // 21.4 Functions of state of the ideal gas 237 // 21.5 Gibbs paradox 240 // 21.6 Heat capacity of a diatomic gas 241 // Exercises 243 // 22 The chemical potential 244 // 22.1 A definition of the chemical potential 244 // 22.2 The meaning of the chemical potential 245 // 22.3 Grand partition function 247 // 22.4 Grand potential 248 // 22.5 Chemical potential as Gibbs function per particle 250 // 22.6 Many types of particle 250 // 22.7 Particle number conservation laws 251 // 22.8 Chemical potential and chemical reactions 252 // 22.9 Osmosis 257 // Further reading 261 // Exercises 262 // 23 Photons 263 // 23.1 The classical thermodynamics of electromagnetic radiation 264 // 23.2 Spectral energy density 265 // 23.3 Kirchhoff’s law 266 // 23.4 Radiation pressure 268 // 23.5 The statistical mechanics of the photon gas 269 // 23.6 Black-body distribution 270 // 23.7 Cosmic microwave background radiation 273 // 23.8 The Einstein A and ? coefficients 274 // Further reading 277 // Exercises 278 // 24 Phonons 279 // 24.1 The Einstein model 279 // 24.2 The Debye model 281 // 24.3 Phonon dispersion 284 // Further reading 287 // Exercises 287 // VIII Beyond the ideal gas 289 // 25 Relativistic gases 290 // 25.1 Relativistic dispersion relation for massive particles 290 // 25.2 The ultrarelativistic gas 290 // 25.3 Adiabatic expansion of an ultrarelativistic gas 293

// Exercises 295 // 26 Real gases 296 // 26.1 The van der Waals gas 296 // 26.2 The Dieterici equation 304 // 26.3 Virial expansion 306 // 26.4 The law of corresponding states 310 // Exercises 312 // 27 Cooling real gases 313 // 27.1 The Joule expansion 313 // 27.2 Isothermal expansion 315 // 27.3 Joule-Kelvin expansion 316 // 27.4 Liquefaction of gases 318 // Exercises 320 // 28 Phase transitions 321 // 28.1 Latent heat 321 // 28.2 Chemical potential and phase changes 324 // 28.3 The Clausius-Clapeyron equation 324 // 28.4 Stability and metastability 329 // 28.5 The Gibbs phase rule 332 // 28.6 Colligative properties 334 // 28.7 Classification of phase transitions 335 // 28.8 The Ising model 338 // Further reading 343 // Exercises 343 // 29 Bose—Einstein and Fermi—Dirac distributions 345 // 29.1 Exchange and symmetry 345 // 29.2 Wave functions of identical particles 346 // 29.3 The statistics of identical particles 349 // Further reading 353 // Exercises 354 // 30 Quantum gases and condensates 358 // 30.1 The non-interacting quantum fluid 358 // 30.2 The Fermi gas 361 // 30.3 The Bose gas 366 // 30.4 Bose-Einstein condensation (???) 367 // Further reading 373 // Exercises 373 // IX Special topics 375 // 31 Sound waves 376 // 31.1 Sound waves under isothermal conditions 377 // 31.2 Sound waves under adiabatic conditions 377 // 31.3 Are sound waves in general adiabatic or isothermal? 378 // 31.4 Derivation of the speed of sound within fluids 379 // Further reading 382 // Exercises

382 // 32 Shock waves 383 // 32.1 The Mach number 383 // 32.2 Structure of shock waves 383 // 32.3 Shock conservation laws 385 // 32.4 The Rankine-Hugoniot conditions 386 // Further reading 389 // Exercises 389 // 33 Brownian motion and fluctuations 390 // 33.1 Brownian motion 390 // 33.2 Johnson noise 393 // 33.3 Fluctuations 394 // 33.4 Fluctuations and the availability 395 // 33.5 Linear response 397 // 33.6 Correlation functions 400 // Further reading 407 // Exercises 407 // 34 Non-equilibrium thermodynamics 408 // 34.1 Entropy production 408 // 34.2 The kinetic coefficients 409 // 34.3 Proof of the Onsager reciprocal relations 410 // 34.4 Thermoelectricity 413 // 34.5 Time reversal and the arrow of time 417 // Further reading 419 // Exercises 419 // 35 Stars 420 // 35.1 Gravitational interaction 421 // 35.2 Nuclear reactions 426 // 35.3 Heat transfer 427 // Further reading 434 // Exercises 434 // 36 Compact objects 435 // 36.1 Electron degeneracy pressure 435 // 36.2 White dwarfs 437 // 36.3 Neutron stars 438 // 36.4 Black holes 440 // 36.5 Accretion 441 // 36.6 Black holes and entropy 442 // 36.7 Life, the Universe, and entropy 443 // Further reading 445 // Exercises 445 // 37 Earth’s atmosphere 446 // 37.1 Solar energy 446 // 37.2 The temperature profile in the atmosphere 447 // 37.3 Radiative transfer 449 // 37.4 The greenhouse effect 452 // 37.5 Global warming 456 // Further reading 460 // Exercises 460 // A Fundamental constants 461 // ? Useful formulae 462 // C Useful

mathematics 464 // C.l The factorial integral 464 // C.2 The Gaussian integral 464 // C.3 Stirling’s formula 467 // C.4 Riemann zeta function 469 // C.5 The polylogarithm 470 // C.6 Partial derivatives 471 // C.7 Exact differentials 472 // C.8 Volume of a hypersphere 473 // C.9 Jacobians 473 // C.10 The Dirac delta function 475 // C.ll Fourier transforms 475 // C.12 Solution of the diffusion equation 476 // C.13 Lagrange multipliers 477 // D The electromagnetic spectrum 479 // E Some thermodynamical definitions 480 // F Thermodynamic expansion formulae 481 // G Reduced mass 482 // H Glossary of main symbols 483 // Bibliography 485 // Index 489

(OCoLC)698875008