THE STEAM ENGINE CONSIDERED AS A THERMODYNAMIC MACHINE
1 Introduction References 1 10 11 11 12 14 2 21 22 23 The Zeroth Law of Thermodynamics Thermal Equilibrium and Temperature An Alternative Form of the Law Absolute Temperature References 3 The First Law of Thermodynamics 18 19 20 20 23 23 23 24 25 29 31 32 33 331 332 333 34 References Mechanical Equivalent of Heat Energy Conservation Law Spaces of Macroscopic Variables Thermodynamic Space Space of Conjugate Variables to Quantification of the Variables of Work 31 32 33 34 35 41 42 45 46 47 48 49 50 51 52 54 55 56 57 60 61 63 64 65 66 69 70 72 73 78 80 80 87 89 92 94 96 97 99 4 41 411 412 42 43 44 45 46 461 462 47 471 472 473 474 48 481 482 49 491 492 493 410 References 5 51 52 521 522 53 531 532 54 541 542 543 544 545 The Second Law of Thermodynamics Carnot’s Theorem Maximum Work Efficiency of Reversible Carnot Cycles The Second Law of Thermodynamics Thermodynamic Temperature Clausius’ Inequality Clausius Entropy for Reversible Processes Calortropy for Irreversible Processes Mathematical Representation of the Second Law of Thermodynamics Integral and Differential Forms of the Thermodynamic Laws Compensated and Uncompensated Heats Variation in Calortropy Compensated Heat and Changes Uncompensated Heat Proposition for Uncompensated Heat Clausius–Duhem Inequality Isolated Systems Non-isolated Systems Extended Gibbs Relations Uncompensated Heat and Constitutive Equations Non-Equilibrium Thermodynamic Functions New Thermodynamic Function Summary Thermodynamics of Global Irreversible Processes The Convexity of Thermodynamics of Composite Systems Thermodynamic Stability of Heterogeneous Systems Equilibrium Conditions Some Examples of Global Processes Global Thermodynamic Forces Examples for Global Constitutive Equations Irreversible Thermodynamics of Neural Networks Neural Networks and Calortropy Production Network of Bromate Oscillators Hebbian Learning Rules Calortropy Production Logic Operations and Calortropy Production 101 109 112 114 114 116 117 117 119 120 121 123 126 127 130 137 140 140 145 148 150 151 153 157 159 163 164 166 168 169 175 176 177 178 References 181 546 References 6 61 62 621 622 623 624 625 63 631 632 633 64 65 7 71 139 111 159 711 712 72 73 74 75 References References 8 81 82 83 84 841 842 85 Examples 851 852 853 Conservation Laws and Evolution Equations Local Field Variables Local Intensive Variables Local Temperature Local Pressure Local Chemical Potentials Local Generalized Potentials The Set of Local Intensive Variables Local Forms of the Conservation Laws Time Derivative of Global Variables Conservation Laws and Balance Equations Local Internal Energy Differential Evolution Equations for Non-Conserved Variables Global Form of the First Law Revisited Local Form of the Second Law of Thermodynamics Local Differential Form for Calortropy Calortropy Balance Equation Calortropy Differential Chemically Reacting Fluids Connection with Equilibrium Thermodynamics Legendre Transformations for Local Variables Other Versions of Irreversible Thermodynamics Local Irreversible Thermodynamics Generalized Thermodynamics Integrating Factor Integrability Conditions and Maxwell's Relations Applications of Maxwell's Relations Symmetry Relations Non-Equilibrium Free Energy Ideal Gas van der Waals Gas Canonical Equation of State Numerical Simulations 183 184 185 185 188 189 190 193 197 202 205 207 208 209 216 219 222 224 224 226 228 230 233 234 239 241 243 251 253 255 257 258 259 264 265 267 268 270 271 272 277 9 91 92 921 922 923 924 93 94 95 96 961 962 963 References 10 101 102 1021 1022 1023 1024 103 1031 1032 1033 1034 104 1041 1042 1043 1044 1045 105 1051 1052 1053 1054 1055 1056 1057 Thermodynamics of Linear Irreversible Processes Clausius Entropy and Linear Irreversible Processes Linearized Constitutive Equations for Fluxes Fluids with a Bulk Viscosity The Navier—Stokes and Fourier Equations Hyperbolic Partial Differential Equations Multi-Component Fluids Ultrasonic Waves in Monatomic Gases Ultrasonic Waves in Rigid Diatomic Gases Viscoelasticity of Fluids Galvanic Cells Galvanic Cells with Liquid Junctions Local Hydrodynamic Equations Calortropy Production in the Galvanic Cell Irreversible Thermodynamics of Steady States Model Generalized Hydrodynamic Equations Reduced Evolution Equations Reduced Variables Reduced Hydrodynamic Equations Navier–Stokes–Fourier Theory Adiabatic Approximation Simple Flows Plane Couette Flow Tube Flow Stick Boundary Conditions Langmuir Boundary Conditions for Flows Shock Waves in Monatomic Gases Generalized Hydrodynamic Equations Reduced Hydrodynamic Equations Boundary Conditions Differential Equations for Reduced Velocity and Temperature Shock Solutions and Shock Structure Shock Waves in Diatomic Gases Generalized Hydrodynamic Equations One-Dimensional Shock Wave Equations Reduced Hydrodynamic Equations Boundary Conditions Differential Equations for Reduced Velocity and Temperature Comparison with Experiment Shock Solutions of the Evolution Equations Two-Dimensional Shock Waves Flow in Microstructures and Nanostructures Generalized Hydrodynamic Equations 106 107 1071 1072 Reduced Hydrodynamic Equations 108 Model Equations for MicroChannel Flow 1081 1082 1083 Profile for the Streamwise Velocity Differential Equation for Approximate Pressure Distribution References Variational Principles Thermodynamic d'Alembert Principle Thermodynamic Lagrangian for Linear Processes Generalized Treatment Downward Scheme Upward Scheme 111 112 113 1131 1132 References Contact Form in Thermodynamics Vector Field Examples in Equilibrium Thermodynamics Ideal Gas Thermodynamics van der Waals Fluid A General Form for f Sheared Non-Equilibrium Real Fluids 121 122 123 1221 1222 1223 References 279 280 281 284 287 288 292 293 296 301 303 310 312 312 316 318 319 320 323 323 324 325 326 332