Fundamentals of Thermodynamics and Applications (eBook)

Title Page 2
Preface 5
Contents 7
Prologue on ideal gases and incompressible fluids 17
Thermal and caloric equations of state 17
“mol” 18
On the history of the equations of state 19
An elementary kinetic view of the equations of state for ideal gases interpretation of pressure and absolute temperature
Objectives of thermodynamics and its equations of balance 23
Fields of mechanics and thermodynamics 23
{/it Mass density, velocity, and temperature} 23
{/it History of temperature} 23
Equations of balance 25
{/it Conservation laws of thermodynamics} 25
{/it Generic equations of balance for closed and open systems} 25
{/it Generic local equation of balance in regular points} 26
Balance of mass 27
{/it Integral and local balance equations of mass} 27
{/it Mass balance and nozzle flow} 27
Balance of momentum 28
{/it Integral and local balance equations of momentum} 28
{/it Pressure} 30
{/it Pressure in an incompressible fluid at rest} 30
{/it History of pressure and pressure units} 31
{/it Applications of the momentum balance} 32
Balance of energy 42
{/it Kinetic energy, potential energy, and four types of internal energy} 42
{/it Integral and local equations of balance of energy} 45
{/it Potential energy} 47
{/it Balance of internal energy} 48
{/it Short form of energy balance for closed systems} 49
{/it First Law for reversible processes. The basis of “pdV - thermodynamics”} 50
{/it Enthalpy and First Law for stationary flow processes} 50
{/it “Adiabatic equation of state” for an ideal gas – an integral of the energy balance} 52
{/it Applications of the energy balance} 53
History of the First Law 69
Summary of equations of balance 71
Constitutive equations 72
On measuring constitutive functions 72
{/it The need for constitutive equations} 72
{/it Constitutive equations for viscous, heat-conducting fluids, vapors, and gas} 72
Determination of viscosity and thermal conductivity 74
{/it Shear flow between parallel plates. Newton’s law of friction} 74
{/it Heat conduction through a window-pane} 76
Measuring the state functions $p(v,T)$ and $u(v ,T)$ 78
{/it The need for measurements} 78
{/it Thermal equations of state} 78
{/it Caloric equation of state} 79
{/it Equations of state for air and superheated steam} 81
{/it Equations of state for liquid water} 82
State diagrams for fluids and vapors with a phase transition 83
{/it The phenomenon of a liquid-vapor phase transition} 83
{/it Melting and sublimation} 85
{/it Saturated vapor curve of water} 85
{/it On the anomaly of water} 88
{/it Wet region and ( p,v) -diagram of water} 90
{/it 3D phase diagram} 90
{/it Heat of evaporation and (h,T)–diagram of water} 91
{/it Applications of saturated steam} 92
{/it Van der Waals equation} 94
{/it On the history of liquefying gases and solidifying liquids} 96
Reversible processes and cycles. “$p$ d$V$ thermodynamics” for the calculation of thermodynamic engines 98
Work and heat for reversible processes 98
Compressor and pneumatic machine. The hot air engine 99
{/it Work needed for the operation of a compressor} 99
{/it Two-stage compressor} 101
{/it Pneumatic machine} 101
{/it Hot air engine} 102
Work and heat for reversible processes in ideal gases. “Iso-processes” and adiabatic processes 103
Cycles 104
{/it Efficiency in the conversion of heat to work} 104
{/it Efficiencies of special cycles} 105
Internal combustion cycles 111
{/it Otto cycle} 111
{/it Diesel cycle} 114
{/it On the history of the internal combustion engine} 116
Gas turbine 117
{/it Brayton process} 117
{/it Jet propulsion process} 118
{/it Turbofan engine} 119
Entropy 120
The Second Law of thermodynamics 120
{/it Formulation and exploitation} 120
{/it Summary} 126
Exploitation of the Second Law 128
{/it Integrability condition} 128
{/it Internal energy and entropy of a van der Waals gas and of an ideal gas} 129
{/it Alternatives of the Gibbs equation and its integrability conditions} 130
{/it Phase equilibrium. Clausius-Clapeyron equation} 132
{/it Phase equilibrium in a van der Waals gas} 134
{/it Temperature change during adiabatic throttling Example: Van der Waals gas} 135
{/it Available free energies} 138
{/it Stability conditions} 140
{/it Specific heat cp is singular at the critical point} 141
A layer of liquid heated from below – onset of convection 142
On the history of the Second Law 146
Entropy as $S=k lnW$ 149
Molecular interpretation of entropy 149
Entropy of a gas and of a polymer molecule 149
Entropy as a measure of disorder 153
Maxwell distribution 154
Entropy of a rubber rod 155
Examples for entropy and Second Law. Gas and rubber 157
{/it Gibbs equation and integrability condition for liquids and solids} 157
{/it Examples for entropic elasticity} 159
{/it Real gases and crystallizing rubber} 160
{/it Free energy of gases and rubber. (p,V)- and(P, L)-curves.} 162
{/it Reversible and hysteretic phase transitions} 164
History of the molecular interpretation of entropy 165
Steam engines and refrigerators 167
The history of the steam engine 167
Steam engines 169
{/it The (T,S)-diagram} 169
{/it Clausius-Rankine process. The essential role of enthalpy} 169
{/it Clausius-Rankine process in a (T, S)-diagram} 171
{/it The (h, s)-diagram} 173
{/it Steam flow rate and efficiency of a power station} 175
{/it Carnotization} 176
{/it Mercury-water binary vapor cycle} 177
{/it Combined gas-vapor cycle} 178
Refrigerator and heat pump 178
{/it Compression refrigerator} 178
{/it Calculation for a cold storage room} 179
{/it Absorption refrigerator} 180
{/it Refrigerants} 181
{/it Heat pump} 182
Heat Transfer 184
Non-Stationary Heat Conduction 184
{/it The heat conduction equation} 184
{/it Separation of variables} 184
{/it Examples of heat conduction} 185
{/it On the history of non-stationary heat conduction} 192
Heat Exchangers 192
{/it Heat transport coefficients and heat transfer coefficient} 192
{/it Temperature gradients in the flow direction} 194
{/it Temperatures along the heat exchanger} 195
Radiation 197
{/it Coefficients of spectral emission and absorption} 197
{/it Kirchhoff’s law} 199
{/it Averaged emission coefficient and averaged absorption number} 200
{/it Examples of thermodynamics of radiation} 203
{/it On the history of heat radiation} 206
Utilization of Solar Energy 207
{/it Availability} 207
{/it Thermosiphon} 208
{/it Green house} 209
{/it Focusing collectors. The burning glass} 211
Mixtures, solutions, and alloys 212
Chemical potentials 212
{/it Characterization of mixtures} 212
{/it Chemical potentials. Definition and relation to Gibbs free energy} 213
{/it Chemical potentials eight useful properties}
{/it Measuring chemical potentials} 216
Quantities of mixing. Chemical potentials of ideal mixtures 217
{/it Quantities of mixing} 217
{/it Quantities of mixing of ideal gases} 219
{/it Ideal mixtures} 220
{/it Chemical potentials of ideal mixtures} 220
Osmosis 221
{/it Osmotic pressure in dilute solutions. Van’t Hoff’s law} 221
{/it Applications of osmosis} 223
Mixtures in different phases 229
{/it Gibbs phase rule} 229
{/it Degrees of freedom} 230
Liquid-vapor equilibrium (ideal) 231
{/it Ideal Raoult law} 231
{/it Ideal phase diagrams for binary mixtures.} 232
{/it Evaporation in the (p,T)-diagram} 234
{/it Saturation pressure decrease and boiling temperature increase} 235
Distillation, an application of Raoult’s law 236
{/it mol as a unit} 236
{/it Simple application of Raoult’s law} 237
{/it Batch distillation} 237
{/it Continuous distillation and the separating cascade} 240
{/it Rectification column} 242
Liquid-vapor equilibrium (real) 244
{/it Activity and fugacity} 244
{/it Raoult’s law for non-ideal mixtures} 245
{/it Determination of the activity coefficient} 245
{/it Determination of fugacity coefficients} 247
{/it Activity coefficient and heat of mixing. Construction of a phase diagram} 247
{/it Henry coefficient} 249
Gibbs free energy of a binary mixture in two phases 251
{/it Graphical determination of equilibrium states} 251
{/it Graphical representation of chemical potentials} 254
{/it Phase diagram with unrestricted miscibility} 254
{/it Miscibility gap in the liquid phase} 256
Alloys 256
{/it ( T , c_{1}) –diagrams} 256
{/it Solid solutions and the eutectic point} 259
{/it Gibbs phase rule for a binary alloy} 260
Ternary Phase Diagrams 260
{/it Representation} 260
{/it Miscibility gaps in ternary solutions} 261
Chemically reacting mixtures 264
Stoichiometry and law of mass action 264
{/it Stoichiometry} 264
{/it Application of stoichiometry. Respiratory quotient RQ} 266
{/it Law of mass action} 266
{/it Law of mass action for ideal mixtures and mixtures of ideal gases} 267
{/it On the history of the law of mass action} 268
{/it Examples for the law of mass action for ideal gases} 269
{/it Equilibrium in stoichiometric mixtures of ideal gases} 271
Heats of reaction, entropies of reaction, and absolute values of entropies 273
{/it The additive constants in u and s} 273
{/it Heats of reaction} 275
{/it Entropies of reaction} 276
{/it Le Chatelier’s principle of least constraint} 277
Nernst’s heat theorem. The Third Law of thermodynamics 277
{/it Third Law in Nernst’s formulation} 277
{/it Application of the Third Law. The latent heat of the transformation gray $/rightarrow$ white in tin} 278
{/it Third Law in PLANCK’s formulation} 279
{/it Absolute values of energy and entropy} 280
Energetic and entropic contributions to equilibrium 280
{/it Three contributions to the Gibbs free energy} 280
{/it Examples for minima of the Gibbs free energy} 282
{/it On the history of the Haber-Bosch synthesis} 284
The fuel cell 285
Chemical Reactions 285
{/it Various types of fuel cells} 286
{/it Thermodynamics} 287
{/it Effects of temperature and pressure} 289
{/it Power of the fuel cell} 289
{/it Efficiency of the fuel cell} 290
Thermodynamics of photosynthesis 291
{/it The dilemma of glucose synthesis} 291
{/it Balance of particle numbers} 292
{/it Balance of energy. Why a plant needs lots of water} 293
{/it Balance of entropy. Why a plant needs air} 295
{/it Discussion} 296
Moist air 298
Characterization of moist air 298
{/it Moisture content} 298
{/it Enthalpy of moist air} 298
{/it Table for moist air} 299
{/it The ($h_{1+x}$ , x)-diagram} 301
Simple processes in moist air 302
{/it Supply of water} 302
{/it Heating} 303
{/it Mixing} 303
{/it Mixing of moist air with fog} 304
Evaporation limit and cooling limit 304
{/it Mass balance and evaporation limit} 304
{/it Energy balance and cooling limit} 305
Two Instructive Examples: Sauna and Cloud Base 307
{/it A sauna is prepared} 307
{/it Cloud base} 308
Rules of thumb 310
{/it Alternative measures of moisture} 310
{/it Dry adiabatic temperature gradient} 311
Pressure of saturated vapor in the presence of air 312
Selected problems in thermodynamics 314
Droplets and bubbles 314
{/it Available free energy} 314
{/it Necessary and sufficient conditions for equilibrium} 315
{/it Available free energy as a function of radius} 315
{/it Nucleation barrier for droplets} 317
{/it Nucleation barrier for bubbles} 318
{/it Discussion} 319
Fog and clouds. Droplets in moist air 319
{/it Problem} 319
{/it Available free energy. Equilibrium conditions} 320
{/it Water vapor pressure in phase equilibrium} 321
{/it The form of the available free energy} 321
{/it Nucleation barrier and droplet radius} 324
Rubber balloons 325
{/it Pressure-radius relation} 325
{/it Stability of a balloon} 328
{/it A suggestive argument for the stability of a balloon} 330
{/it Equilibria between interconnected balloons} 333
Sound 335
{/it Wave equation} 335
{/it Solution of the wave equation, d’Alembert method} 338
{/it Plane harmonic waves} 339
{/it Plane harmonic sound waves} 340
Landau theory of phase transitions 342
{/it Free energy and load as functions of temperature and strain: Phase transitions of first and second order} 342
{/it Phase transitions of first order} 342
{/it Phase transitions of second order} 345
{/it Phase transitions under load} 347
{/it A remark on the classification of phase transitions} 347
Swelling and shrinking of gels 348
{/it Phenomenon} 348
{/it Gibbs free energy} 350
{/it Swelling and shrinking as function of temperature} 353
Thermodynamics of irreversible processes 356
Single fluids 356
{/it The laws of FOURIER and NAVIER-STOKES} 356
{/it Shear flow and heat conduction between parallel plates} 358
{/it Absorption and dispersion of sound} 360
{/it Eshelby tensor} 362
Mixtures of Fluids 364
{/it The laws of Fourier, Fick, and Navier-Stokes} 364
{/it Diffusion coefficient and diffusion equation} 367
{/it Stationary heat conduction coupled with diffusion and chemical reaction} 369
Flames 371
{/it Chapman-Jouguet equations} 371
{/it Detonations and flames} 373
{/it Equations of balance inside the flame} 374
{/it Dimensionless equations} 376
{/it Solutions} 377
{/it On the precarious nature of a flame} 379
A model for linear visco-elasticity 379
{/it Internal variable} 379
{/it Rheological equation of state} 381
{/it Creep and stress relaxation} 382
{/it Stability conditions} 384
{/it Irreversibility of creep} 384
{/it Frequency-dependent elastic modulus and the complex elastic modulus} 386
Shape memory alloys 387
{/it Phenomena and applications} 387
{/it A model for shape memory alloys} 391
{/it Entropic stabilization} 392
{/it Pseudoelasticity} 395
{/it Latent heat} 398
{/it Kinetic theory of shape memory} 400
{/it Molecular dynamics} 404
Name and subject index 407