THE THEORY OF HEAT
Part I Foundations 1 1 Thermodynamic System and First Law 3 11 Historical Introduction 3 12 Thermodynamic System 5 13 State, Variables and State Functions 5 14 Processes and Change of State 7 15 Extensive and Intensive Quantities 8 16 First Law of Thermodynamics 9 17 Thermodynamics and Mechanics 11 18 Internal Energy 13 19 Damped Harmonic Oscillator 16 110 Worked Solutions 18 Exercises 23 2 Entropy and Second Law 26 21 Historical Introduction 26 22 Temperature 28 23 Heat and Entropy 29 24 Second Law of Thermodynamics 31 25 Simple System 32 26 Closed and Rigid Simple System 35 27 Adiabatic and Closed Mechanical System 36 28 Open, Rigid and Adiabatic System 37 29 Closed Simple System 37 210 Open, Rigid and Diathermal System 39 211 Worked Solutions 41 Exercises 46 3 Thermodynamics of Subsystems 49 31 Historical Introduction 49 32 Rigid and Impermeable Diathermal Wall 50 v 33 Moving, Impermeable and Diathermal Wall 53 34 Rigid and Permeable Diathermal Wall 55 35 Movable and Permeable Diathermal Wall 58 36 Worked Solutions 59 Exercises 67 4 Thermodynamic Potentials 70 41 Historical Introduction 70 42 Fundamental Relations 71 43 Legendre Transformation 74 44 Thermodynamic Potentials 76 45 Equilibrium of Subsystems Coupled to a Reservoir 79 46 Heat and Work of Systems Coupled to Reservoirs 82 47 Maxwell Relations 84 48 Worked Solutions 87 Exercises 96 Part II Phenomenology 101 5 Calorimetry 103 51 Historical Introduction 103 52 Thermal Response Coefficients 105 53 Third Law of Thermodynamics 108 54 Mayer Relations 109 55 Specific Heat of Solids 110 56 Ideal Gas 111 57 Thermal Response Coefficients of the Ideal Gas 112 58 Entropy of the Ideal Gas 114 59 Worked Solutions 118 Exercises 127 6 Phase Transitions 129 61 Historical Introduction 129 62 The Concavity of Entropy 131 63 The Convexity of Internal Energy 133 64 Stability and Entropy 135 65 Stability and Thermodynamic Potentials 137 66 Phase Transitions 139 67 Latent Heat 143 68 The Clausius–Clapeyron Equation 144 69 Gibbs Phase Rule 145 610 Van der Waals Gas 147 611 Worked Solutions 151 Exercises 160 7 Heat Engines 166 71 Historical Introduction 166 72 Thermal Machine 168 73 Carnot Cycle 171 74 Reversible Processes on an Ideal Gas 174 75 Carnot Cycle for an Ideal Gas 176 76 Efficiency and Coefficients of Performance 179 77 Endoreversible Carnot Cycle 181 78 Stirling Engine 183 79 Heat Pump and Refrigerator 185 710 Worked Solutions 187 Exercises 196 8 Chemistry and Electrochemistry 203 81 Historical Introduction 203 82 Chemical Reactions 204 83 Matter Balance and Chemical Dissipation 208 84 Molar Volume, Entropy and Enthalpy 209 85 Mixture of Ideal Gases 212 86 Osmosis 216 87 Electrochemistry 218 88 Worked Solutions 223 Exercises 232 Part III Continuous Media 239 9 Matter and Electromagnetic Fields 241 91 Historical Introduction 241 92 Insulators and Electromagnetic Fields 243 93 Conductors and Electromagnetic Fields 250 94 Conductor and External Electromagnetic Fields 259 95 Adiabatic Demagnetisation 262 96 Worked Solutions 266 Exercises 273 10 Thermodynamics of Continuous Media 277 101 Historical Introduction 277 102 Continuity Equations 278 103 Evolution Equations 287 104 Worked Solutions 298 Exercises 304 11 Thermodynamics of Irreversible Processes 308 111 Historical Introduction 308 112 Linear Empirical Relations 310 113 Chemical Reactions and Viscous Friction 313 114 Transport 314 115 Fluid Dynamics 331 116 Worked Solutions 333 Exercises 349 Part IV Exercises and Solutions 361 1 Thermodynamic System and First Law 363 11 State Function: Mathematics 363 12 State Function: Ideal Gas 363 13 State Function: Rubber Cord 364 14 State Function: Volume 364 15 Cyclic Rule for the Ideal Gas 366 16 Evolution of Salt Concentration 366 17 Capilarity: Contact Angle 368 18 Energy: Thermodynamics Versus Mechanics 369 19 Damped Harmonic Oscillator 371 2 Entropy and Second Law 372 21 Entropy as a State Function 372 22 Work as a Process-Dependent Quantity 373 23 Bicycle Pump 373 24 Rubbing Hands 374 25 Heating by Stirring 375 26 Swiss Clock 376 27 Reversible and Irreversible Gas Expansion 378 3 Thermodynamics of Subsystems 379 31 Thermalisation of Two Separate Gases 379 32 Thermalisation of Two Separate Substances 380 33 Diffusion of a Gas through a Permeable Wall 381 34 Mechanical Damping by Heat Flow 382 35 Entropy Production by Thermalisation 385 36 Entropy Production by Heat Transfer 385 37 Thermalisation by Radiation 386 4 Thermodynamic Potentials 388 41 Adiabatic Compression 388 42 Irreversible Heat Transfer 388 43 Internal Energy as Function of T and V 389 44 Grand Potential 390 45 Massieu Functions 390 46 Gibbs–Helmoltz Equations 391 47 Pressure in a Soap Bubble 392 48 Pressure in a Droplet 393 49 Isothermal Heat of Surface Expansion 394 410 Thermomechanical Properties of an Elastic Rod 395 411 Chemical Power 396 5 Calorimetry 399 51 Heat Transfer as a Function of V and p 399 52 Bicycle Pump 399 53 Heat Transfer at Constant Pressure 400 54 Specific Heat of a Metal 401 55 Work in Adiabatic Compression 401 56 Slopes of Isothermal and Adiabatic Processes 402 57 Adsorption Heating of Nanoparticles 402 58 Thermal Response Coefficients 403 6 Phase Transitions 405 61 Melting Ice 405 62 Cooling Water with Ice Cubes 405 63 Wire through Ice without Cutting 406 64 Dupré’s Law 408 65 Hydropneumatic Accumulator 408 66 Positivity of Thermal Response Coefficients 410 67 Heat Pipe 412 68 Vapour Pressure of Liquid Droplets 413 69 Melting Point of Nanoparticles 414 610 Work on a van der Waals Gas 416 611 Inversion Temperature of the Joule–Thomson Process 416 612 Lever Rule 417 613 Eutectic 418 7 Heat Engines 420 71 Refrigerator 420 72 Power Plant Cooled by a River 420 73 Braking Cycle 422 74 Lenoir Cycle 424 75 Otto Cycle 426 76 Atkinson Cycle 429 77 Refrigeration Cycle 432 78 Rankine Cycle 433 79 Rankine Cycle for a Biphasic Fluid 436 8 Chemistry and Electrochemistry 439 81 Oxidation of Ammonia 439 82 Acetylene Lamp 440 83 Coupled Chemical Reactions 440 84 Variance 442 85 Enthalpy of Formation 443 86 Work and Heat of a Chemical Reaction 444 87 Mass Action Law: Esterification 445 88 Mass Action Law: Carbon Monoxide 445 89 Entropy of Mixing 447 810 Raoult’s Law 448 811 Boiling Temperature of Salt Water 450 812 Battery Potential 451 813 Thermogalvanic Cell 452 814 Gas Osmosis 452 815 Osmosis Power Plant 454 9 Matter and Electromagnetic Fields 456 91 Vapour Pressure of a Paramagnetic Liquid 456 92 Magnetic-Field Induced Adsorption or Desorption 457 93 Magnetic Battery 458 94 Electrocapilarity 459 95 Magnetic Clausius–Clapeyron Equation 460 96 Magnetocaloric Effect 461 97 Kelvin Probe 462 98 Electromechanical Circuit 464 10 Thermodynamics of Continuous Media 467 101 Chemical Substance Balance 467 102 Pressure Time Derivative and Gradient 467 103 Oil and Water Container 469 104 Floating Tub Stopper 469 105 Temperature Profile of the Earth’s Atmosphere 471 106 Stratospheric Balloon 473 107 Velocity Field Inside a Pipe 474 108 Divergence of a Velocity Field 475 11 Thermodynamics of Irreversible Processes 478 111 Heat Diffusion Equation 478 112 Thermal Dephasing 479 113 Heat Equation with Heat Source 480 114 Joule Heating in a Wire 481 115 Thomson Heating in a Wire 482 116 Heat Exchanger 483 117 Harman Method 486 118 Peltier Generator 487 119 ZT Coefficient of a Thermoelectric Material 492 1110 Transverse Transport Effects 495 1111 Hall Effect 497 1112 Heat Transport and Crystal Symmetry 498 1113 Planar Ettingshausen Effect 499 1114 Turing Patterns 502 1115 Ultramicroelectrodes 506 1116 Effusivity 510 References 515