Hari Dass, N.D. The principles of thermodynamics 2014 digitalisiert durch: IDS Basel Bern
Preface Guide for readers and teachers xiii xv Chapter 1 The Beginnings 1 1.1 Temperature and 2 1.1.1 Uniform temperature 3 1.1.2 temperature scales 4 1.1.3 Materials for thermometry 5 1.2 Ideal laws 7 1.2.1 The Kelvin scale 9 1.2.2 gases 1.3 Heat and specific heats 1.3.1 heat 12 1.3.2 States and 13 1.3.3 Some examples 15 1.4 Sadi the of heat 17 Infinitesimal andfinitecycles 26 1.5 engines and the Clapeyron Equation 28 1.6 Problems 32 Chapter 2 First E = Mc 2 of Thermodynamics 33 The fall of the caloric 33 2.2 The path to the first law 34 2.3 The first law of thermodynamics 37 2.4 Some applications of thefirstlaw 40 2.4.1 Internal energy of ideal gases 41 2.4.2 Isochoric changes 41 2.4.3 Isobaric changes 41 2.4.4 Adiabatic changes in an ideal gas 42 2.4.5 Isothermal changes 43 2.4.6 Heats transformation 43 2.4.7 43 2.5 Problems 48 2.6 Suggested reading for this book in 49
3 The Second and Third Laws 51 3.1 Perpetuum mobiles 52 3.1.1 Perpetual machines of thefirstkind 52 3.1.2 Perpetual machines of the second kind 53 3.2 The entropy the first part of second law 53 3.2.1 A first law for ideal gases 53 3.2.2 A consequence of the entropy axiom 54 3.3 Entropy axiom and universality of Carnot cycles 55 3.3.1 Ideal gas Carnot 59 3.3.2 Composition of Carnot cycles 60 3.4 Historical of second law 61 3.4.1 Consequences of Clausius Inequality 63 3.5 Second law and 65 3.5.1 Second law and arrow of 69 3.5.2 Entropy and disorder 70 3.5.3 Entropy and Information 70 3.6 An absolute scale of temperature 70 3.7 Applications first and second laws 72 3.8 Third law of thermodynamics - the Nernst-Planck postulate 79 3.9 Problems 85 Chapter 4 Carnot Cycles - The Turing Machines of Thermodynamics 87 4.1 The gas Carnot cycles 87 4.1.1 The ideal gas cycles 87 4.1.2 The van cycle 88 4.2 The Carnot cycle 89 4.3 The Stirling engine 90 4.4 The Otto cycle 92 4.4.1 The Diesel cycle 93 4.5 The Brayton cycle 93 4.5.1 The magnetic Brayton cycle 94 4.6 Carnot cycle with photons 96 The Thermodynamics of the radiation field 96 4.6.2 Photon Carnot cycle 99 4.6.3 The thermodynamic gateway to world 100 4.7 Problems 101 Chapter 5 Specific Heats: Magnificent Bridges 103 5.1 A brief history 103 5.2 Varieties of specific heats 105 Negative specific heats 106 5.3 Specific heats and the third law 107
Specific heats and cooling powers 107 5.4 Specific heats and microscopics 108 5.5 Specific heats herald quantum theory! 109 Einstein and specific heats 109 5.5.2 Debye Theory 5.5.3 Specific heats of quantum ideal gases 5.6 Problems Chapter 6 Structure of Thermodynamic Theories Extensive and intensive variables: general 122 6.2 The Fundamental Equations 124 Intensive variables and the fundamental 125 6.2.2 The Euler relations 126 6.2.3 The relations 127 6.3 True equations of State 127 6.4 Multicomponent Systems 128 6.5 Entropy of and the Gibbs paradox 130 Extensivity revisited 132 6.6 Worked out examples 133 Fundamental equations and equations of State 133 6.6.2 Gibbs-Duhem relations 135 6.7 Axiomatic intensive variables and equilibrium 6.7.1 Stability of equilibrium 136 6.8 Problems 137 Chapter 7 Thermodynamic Potentials and Maxwell Relations 7.1 Thermodynamic potentials 139 7.1.1 Internal energy and enthalpy 140 Helmholtz free energy 140 7.1.3 Gibbs free energy 142 7.2 Maxwell 's relations 143 7.2.1 How different potentials? 145 7.2.2 Inclusion of potential 146 7.3 Problems 147 Chapter 8 Magnetic Systems 8.1 Introduction 149 8.2 Thermodynamic potentials Inclusion of PdV and terms in du 163 8.2.2 Magnetic Euler relations 8.2.3 Counting the magnetic potentials 164 8.2.4 PdV vs 8.2.5 Equation of for magnetic 166
x Contents 8.2.6 Equilibrium conditions 169 8.3 Problems 170 Chapter 9 Dilute Solutions 171 General considerations 171 9.2 Mixing revisited 174 9.3 Osmotic pressure 177 9.4 Vapor pressure and boiling point of 180 9.5 Freezing point of dilute 185 9.6 Problems 186 Chapter 10 Phases and Their Equilibria 189 10.1 The Gibbs phase 189 10.2 Phases of water 192 10.3 Salt water phase diagram 195 10.4 Phases of Carbon 196 10.5 Phase Diagram 197 10.6 Phase Diagram 198 10.7 QCD Phase Diagram 199 10.8 Superconducting Phase Transitions 200 10.9 Superconductor Phase Diagram 202 10.10 Problems 203 Chapter 11 The Clapeyron Equation 205 original treatment 205 Clausius's improvement 205 More modern approaches 206 Other 207 Freezing curves 209 Anomalous freezing curves 210 Boiling and Sublimation curves 210 near absolute zero The Dew, frost and relative An 212 11.5 Temperature dependence of latent heats 215 11.5.1 treatment 216 Boiling points of dilute 217 Breakdown of the Clapeyron equation 218 Magnetic Clapeyron equation 219 Superconducting transitions 221 11.9 Problems 226
Chapter 12 The van der Equation 229 12.1 Thermodynamic aspects 230 12.1.1 Thermodynamic potentials 231 12.1.2 Various isoparametric processes 233 12.1.3 Properties the vdw isotherms 235 12.2 Existence of Phases in the vdw 239 12.2.1 The Maxwell construction 242 12.2.2 and unstable states of the vdw 244 12.2.3 Phases vdw system 246 12.3 Negative pressures in vdw Systems 247 12.4 Surface tension 248 12.5 Thermodynamics of inhomogeneous substances 250 12.5.1 van der Waals theory of surface tension 251 12.5.2 Surface thermodynamics in vdw theory 254 12.6 Revisiting the bubble pressure 255 12.7 Problems 257 Chapter 13 The Critical Point 259 13.1 Overview 259 13.2 Critical properties of 261 13.2.1 The coexistence curve 13.2.2 Latent heat 262 13.2.3 Surface tension 263 13.3 Critical behaviour of van der Waals theory 264 13.3.1 Critical exponents of vdw theory 267 13.3.2 Even more exponents 268 13.3.3 Beyond the critical region of vdw theory 269 13.3.4 From van der Waals to Wilson via Landau 271 13.3.5 The group 272 13.3.6 Renormalization group inspired 13.4 Problems 274 Chapter 14 to Absolute Zero 275 14.1 Standard methods of refrigeration 275 14.1.1 power 276 14.2 Helium cryostats 277 14.2.1 He4cryostat 278 14.2.2 279 14.3 Dilution refrigeration 280 Thermodynamics of He3-He4 mixtures 280 14.3.2 Cooling power of dilution refrigerators 284 14.3.3 The dilution refrigerator 285 14.3.4 Dilution refrigeration: designs 285
14.4 Magnetic cooling 288 14.4.1 Principles of adiabatic cooling 288 14.4.2 Adiabatic demagnetization 289 14.4.3 Electronic demagnetization: some results 292 14.4.4 Nuclear demagnetization: some results 294 14.4.5 Cascade nuclear demagnetization 295 14.4.6 Further 295 14.5 Pomeranchuk cooling 295 14.5.1 The principle of cooling 297 14.5.2 298 14.6 Problems 298 Chapter 15 Entropy Constants 299 15.1 reactions 300 15.2 Entropy constants for solids 302 15.3 Two verifications of the Sackur-Tetrode 307 15.4 The entropy constants gases 309 15.5 Problems 311 Chapter 16 Some Mathematical Aspects of Thermodynamics 313 16.1 Introduction 313 16.2 Differentials and derivatives 314 16.2.1 Partial derivatives 314 16.2.2 Important properties of partial derivatives 315 16.2.3 316 16.3 Jacobian matrices and Jacobians 317 16.3.1 Some important properties of Jacobians 317 16.3.2 318 16.3.3 Maxwell relations and Jacobians 319 16.3.4 Thermodynamic potentials and Jacobians 16.3.5 Another application to thermodynamics 320 16.4 Differential in thermodynamics 320 16.4.1 Some applications to thermodynamics 321 References 323 Index 327 Name Index 337