Bibliography
A. LARGE GENERAL WORKS AND TEXTBOOKS
J. W. Gibbs. Collected Works , vol. I, Yale University Press, New Haven, 1957. J. D. van der Waals and Ph. Kohnstamm. Lehrbuch der Thermostatik , Barth,
Leipzig, 1927.
W. Schottky, H. Ulich and C. Wagner. Thermodynamik , Springer, Berlin, 1929.
M. Planck. Vorlesungen uber Thermodynamik , 11th ed., De Gmyter, Berlin, 1964.
G. N. Lewis and M. Randall. Thermodynamics , 2nd ed., McGraw-Hill, New York, 1961.
M. W. Zemanski. Heat and Thermodynamics , 4th ed., McGraw-Hill, New York, 1957.
I. Prigogine and R. Defay. Chemical Thermodynamics, Longmans, Green, London, 1954.
A. B. Pippard. The Elements of Classical Thermodynamics , Cambridge University Press, Cambridge, 1957.
R. Haase. Thermodynamik der Mischphasen , Springer, Berlin, 1956.
H. Callen. Thermodynamics , Wiley, New York, 1960.
J. G. Kirkwood and I. Oppenheim. Chemical Thermodynamics , McGraw-Hill, New York, 1961.
E. A. Guggenheim. Thermodynamics , 5th ed., North-Holland, Amsterdam, 1967.
B. AXIOMATICS
A. Land6. Die Caratheodory'sche Axiomatik {Geiger-Scheel Handbuch der Physik), vol. IX, Springer Verlag, Berlin, 1926.
G. Falk and H. Jung. Axiomatik der Thermodynamik (Handbuch der Physik, (S. Fliigge Ed.) Vol. III. 2), Springer Verlag, Berlin, 1959.
P. T. Landsberg, Thermodynamics , Interscience, New York, 1961.
R. Giles. Mathematical Foundations of Thermodynamics, Pergamon, Oxford, 1964.
H. A. Buchdahl. The Concepts of Classical Thermodynamics , Cambridge University Press, Cambridge, 1966.
L. Tisza. Generalized Thermodynamics , M.I.T. Press, Cambridge (Mass.), 1966.
C. HETEROGENEOUS EQUILIBRIA
H. W. Bakhuis Roozeboom. Die heterogenen Oleichgewichte , Friedr. Viehweg, Braunschweig, 1901-1911.
M. Hansen. The Constitution of Binary Alloys , 2nd ed., McGraw-Hill, New York, 1958.
D. NERNST’S HEAT THEOREM
W. Nernst. Theoretische und experimentelle Grundlagen des neuen Wdrmesatzes, 2nd ed., W. Knapp, Halle, 1924.
K. Bennewitz. Der Nernst'sche Wdrmesatz {Geiger-Scheel Handbuch der Physik)t vol. IX , Springer Verlag, Berlin, 1926.
F. Simon. Ergebnisse der exakten Naturwissenschaften, 9, 222, Springer, Berlin, 1930.
F. Simon. Science Museum Handbook , 3, 61, 1937.
J. Wilks. The Third Law of Thermodynamics , Oxford University Press, Oxford, 1961.
E. HIGHER ORDER TRANSITIONS
L. Tisza. On the General Theory of Phase Transitions (Phase Transformations in Solids, R. Smoluchowski, J. E. Mayer and W. A. Weyl, Eds.), p. 1, Wiley, New York, 1951.
F. SOLIDS
W. Voigt. Lehrbuch der Kristallphysik , Teubner, Leipzig, 1928.
A. Sommerfeld. Mechanik der deformierbaren Medien (Vorlesungen liber theoretische Physik), vol. II, 4th ed., Akad. Verlagsges., Geest and Portig K.-G., Leipzig, 1957.
L. D. Landau and E. M. Lifshitz. Theory of Elasticity (Course of Theoretical Physics), vol. 7, Pergamon, Oxford, 1959.
G. SYSTEMS IN ELECTRIC AND MAGNETIC FIELDS
A. Sommerfeld. Elektrodynamik (Vorlesungen liber Theoretische Physik), vol. Ill, 3rd ed., Akad. Verlagsges., Leipzig, 1961.
L. D. Landau and E. M. Lifshitz. Electrodynamics of Continuous Media
(Course of Theoretical Physics), vol. 8, Pergamon, Oxford, 1960. J. D. Jackson. Classical Electrodynamics , Wiley, New York, 1962.
W. Kanzig. Ferroelectrics and Antiferroelectrics (Solid State Physics, F. Seitz
and D. Turnbull, Eds.), vol. 4, p. 1, Academic, New York, 1957.
E. Fatuzzo and W. J. Merz. Ferroelectricity, North Holland, Amsterdam, 1967.
J. H. van Vleck. Theory of Electric and Magnetic Susceptibilities, Oxford University Press, Oxford, 1952.
H. M. Rosenberg. Low Temperature Solid State Physics, Oxford University
Press, Oxford, 1963.
P. G. de Gennes. Superconductivity of Metals and Alloys , Benjamin, New York, 1966.
H. ELECTROCHEMICAL SYSTEMS
H. Falkenhagen. Elektrolyte , Hirzel, Leipzig, 1953.
H. S. Hamed and B. Owen. The Physical Chemistry of Electrolytic Solutions, 3rd ed., Reinhold Publ. Corporation, New York, 1958.
R. A. Robinson and R. H. Stokes. Electrolyte Solutions , 2nd ed., Butterwortli, London, 1959.
I. STATISTICAL THERMODYNAMICS
R. H. Fowler and E. A. Guggenheim. Statistical Thermodynamics , Cambridge University Press, Cambridge, 1949.
A. Munster. Statistical Thermodynamics , 2nd ed., Springer Verlag, BerlinNew York, 1969.
J. TABLES
F. Rossini. Selected Values of Chemical Thermodynamic Properties, Carnegie Press, Washington, 1952.
К. K. Kelley. Entropies of Inorganic Substances , Bur. of Mines Bull. 477, U.S.G.P.O., 1950.
К . K. Kelley. High Temperature Heat Content , Heat Capacity and Entropy Data, Bur. of Mines Bull. 476, U.S.G.P.O., 1949.
Landolt-Bomstein. Zahlenwerte und Funktionen , 6th ed., vol. II, 2nd-4th parts, Springer Verlag, Berlin, 1956-1964.
K. MATHEMATICAL AIDS
H. Margenau and G. M. Murphy. The Mathematics of Physics and Chemistry , 2nd ed., D. Van Nostrand Company Inc., New York, 1962.
Index
Absolute temperature 33
Thomson’s definition 12 zero, unattainability of 150
Activities 137
Activity coefficients 136 for solid solutions 305 of electrolyte, mean 286
determination 304 of ions 285
of solid mixed phases 137, 139 of solvent 285 standardization 137
Adiabatic curve 20
demagnetization 154, 270 process 12
wall 20 Affinity 48
Amount of substance 316 Azeotropic
curve 118 mixtures 117 point 125
Barometric height equation 312 Binodal curve 178
Bivariant equilibria 124^127 Boiling point of solvent, elevation
319-322
Boudouard equilibrium 138 Bridgeman’s method 95-97
Caratheodory’s principle 30 Carnot
cycle 12 theorem 11
Cells—see Galvanic cell and Half-cell
Celsius scale 22 Characteristic function 69 Chemical
constants 338 equilibrium,
general conditions for 129, 131 in gravitational field 310 stability 176, 177
potential 50, 76, 103
for gases, standard values 133 in presence of electric field 246 of electrolyte 287
of liquid mixtures, standard states 136
of solvent 107 reactions,
phase rule in 140 thermodynamic calculation
141-144 Clausius-Clapeyron equation 120
generalized,
for bivariant and multivariant equilibria 125
for univariant equilibrium 123 Clausius’
inequality 16 principle 9 relation 324
Coefficients,
activity 136, 137, 139, 285, 286, 304, 305
elastic compliance 231 elastic stiffness 229, 341 Joule-Thomson 101
of thermal expansion 95 osmotic 288 stoichiometric 46 thermal strain 340
Coefficients (contd .) thermal stress 340 thermodynamic 205 work 46
Co-existence curves 119, 178 Compressibility,
isentropic 166, 170 isothermal 170, 237
Congruently melting compound 334 Conjugate parameters 76 Connodals 178
Consolute point, lower 179 upper 179
Contact equilibrium 49 Corresponding states, principle of 158 Critical
opalescence 192 parameters 213 phase 178
degrees of freedom 182 general equations 188 transformation of equations
189-192 phenomena 191 points 178
and higher-order transitions, Tisza’s theory 208-215 temperature—see Temperature
Cryoscopic constant 322
Crystalline solid, vapour pressure 337 Crystals,
ferroelectric 255 pyroelectric 254
Curie point, ferroelectric 255 Curie-Weiss law 271
Cyclic process 8
reversible, efficiency of 10
Dalton’s law of partial pressures 131 Deformation,
infinitesimal, quasi-static work done in 226
small, mathematical description 217
Degree of
dissociation, dependence of molar heat capacity 336
long-range order 202
Degrees of freedom of a critical phase 182
Densities 73
Diamagnetic substances 269 Diathermic wall 20 Dielectric
constant 239 tensor 239
Diesel engine 325 Differential equations
for isothermal vapour pressure diagram 333
for temperature dependence of heat of reaction 335 Differentials—see also Pfaff differ
entials complete 26 incomplete 25
Donnan equilibrium 293-295 Dystectic points 128, 334
Ebullioscopic constant 322 Ehrenfest equations for second order
transitions 198, 277 Einstein condensation 332 Elastic
compliance coefficients, isothermal 231
stiffness coefficients, isothermal 229 Electrical
neutrality, condition of 280 susceptibility 242
Electric field,
chemical potentials in presence of 246
fundamental equation for body in 245
Gibbs free energy for body in 246 Helmholtz free energy for body in
246
quasi-static work done on system in 242, 244
Electrocaloric effect 251 Electrochemical
equilibrium,
general conditions for 282-284 in galvanic cell 300
potential 283 systems 279
Electrochemical systems (contd.) fundamental equation 283
Electrode potentials, single 286, 303 Electrode, standard 302 Electrolytes 279
activity coefficients, mean 286 determination 304
binary 280
volatile, vapour pressure equilib rium of aqueous solution 290
chemical potential 287 mole fraction 287
mean 287 stoichiometric 287
solutions, membrane equilibria 292-295
strong, solutions of 284-292 Electromotive force (e.m.f.),
of galvanic cell 297 standard values,
for galvanic cell 301 for half-cell 303
temperature dependence 304 Electrostriction 247
Energy—see also Free energy internal 9, 23 representation 68, 76
stability conditions 165 Enthalpy 78—see also Heat content
of body in magnetic field 268 standardization 155 standard state 155
Entropy 13, 33, 50 calorimetric 157 conventional zero point 156 of dilution 107 representation 68 spectroscopic 157 standardization 156 standard state 156
Equations,
Clausius-Clapeyron 120, 123, 125 Ehrenfest 198, 277
fundamental 50, 67, 68, 69, 74, 76, 83, 228, 245, 268, 283
Gibbs-Duhem 69, 75, 78, 104, 105, 107, 229
Gibbs-Helmholtz 91, 92, 134, 149, 304
Equations {contd.) Kirchhoff 320 of state 69, 72 caloric 72 thermal 72
thermal 22, 229, 316 van der Waals 324 van’t Hoff 135 vapour pressure 333
Equilibrium 6, 52 bivariant 124-127 Boudouard 138 chemical,
general conditions 129, 131 in gravitational field 310 stability 176, 177
conditions,
for constant entropy, volume and mole number 88
for constant temperature, pressure and mole number 88
for constant temperature, volume and mole number 88
for homogeneous fluid in gravi tational field 310
general, for heterogeneous systems 109-111
transformation 85-90 constants 132
contact 49 Donnan 293-295 electrochemical,
general conditions 282-284 in galvanic cell 300
frozen 145
Gibbs’, conditions 56 hydrostatic, condition 311 invariant 119
membrane 111-113 non-osmotic 293
of electrolyte solutions 292-295 osmotic 112, 293-295
metastable 62, 160 multivariant 124-127 neutral 62 sedimentation,
equations for 312
in centrifugal field 313 stable 61
Equilibrium (contd.) thermal 21 thermodynamic 52
for galvanic cell 297 univariant 120 unstable 62
vapour pressure, of aqueous solution of volatile binary elec
trolyte 290 Equivalence principle 8 Euler’s theorem 67 Eutectic mixtures 123
Extensive parameters 49, 68
Faraday 283
Ferroelectric crystals 255 Curie point 255
First Law of thermodynamics—see Thermodynamics
First-order transitions—see Transi tions
Force, generalized 46 Free energy
Gibbs 81
for body in electric field 246 for solids 230
mean molar 102
of body in magnetic field 269 Helmholtz 80
for body in electric field 246 for solids 230
of body in magnetic field 268 of dilution 107
Freezing point, of solvent, lowering 322
Fugacities 132
Fundamental equation 50, 67, 68, 76, 83
for body in electric field 245 for electrochemical systems 283 for solids 228
of body in magnetic field 268 per mole 74
properties 69
Galvanic cell—see also Half-cell definition 296
Galvanic cell {contd.) electrochemical equilibrium,
general condition for 300 electromotive force (e.m.f.) 297
standard value 301 irreversible 296, 304 reversible 296
thermodynamic equilibrium 297 Gas
ideal 22
one-component, thermal equation of state 316
reactions, homogeneous 131-136, 143
thermometer scale 22 Gases,
chemical potentials 133 ideal mixture 131
Gay-Lussac’s streaming experiment 36, 38, 326
Generalized force 46 Gibbs-Dalton law 133 Gibbs-Duhem equation 69, 75, 78
for solids 229 generalized 104
isothermal-isobaric form 105, 107 Gibbs’ equilibrium conditions 56 Gibbs free energy— see Free energy Gibbs-Helmholtz equation 91, 304
integration 92, 143, 149 Gibbs-Konowalow rule, generalized
125
Gibbs’ phase rule 114 Gibbs’ stability criterion 162 Gough-Joule effect 342 Grand potential 82
Half-cell 302—see also Galvanic cell standard e.m.f. values 303
Heat 24 capacity,
at constant volume 71 molar,
at constant pressure 80, 95, 169 at constant strain 340
at constant stress 340
at constant volume 25, 99, 165, 169
Heat (contd .)
capacity, molar {contd.)
at saturation vapour pressure 333
dependence on degree of dissoci ation 336
conducting wall 20
content 78—see also Enthalpy of dilution 107
of melting 120
of phase change 120 of reaction, differential
equations for temperature de pendence 335
of vaporization 120 pump 18 ‘uncompensated’ 16
Helium, A-transition 194, 199 Helmholtz free energy— see Free
energy
Helmholtz’ fundamental theorem of kinematics 218
Hess’ Law 335
Heterogeneous reactions 138-140
systems, stability conditions 171-173
Homogeneous
fluid, equilibrium conditions in gravitational field 310
functions 67
gas reactions 143
solution reactions, in liquid state 136, 137
system 7, 308
Hydrostatic equilibrium, condition for 311
Hyperstructure transitions—see Transitions
Incongruently melting compound 335 Ideal
gas 22
solution, dilute 137 Indifference conditions 117 Indifferent curve 118
Integrating factor, condition for existence 26
Intensive parameters 49, 68, 76
Internal
energy—see Energy parameters 53
Invariant equilibria 119 Inversion curve 329
Ions, activity coefficients of 285 Irreversible processes 15 Isentropic
compressibility 166, 170 elastic stiffness coefficients 341 processes 13
Isothermal
compressibility 95, 170, 237 elastic compliance coefficients 231 elastic stiffness coefficients 229 process 12
vapour pressure diagram, differen tial equations 333
Isotherms 23, 178, 184
Jacobi determinants, method using 97-100
J oule-Thomson coefficient 101 effect 100-102
integral (total) 331
Kelvin scale 12
Kinematics, Helmholtz’ fundamental theorem 218
Kirchhoff’s equation 320 Konowalow’s rules 126
Lagrange method of undetermined multipliers 110, 289, 291, 310
Lam6 constants 234 Law,
Curie-Weiss 271
Dalton’s law of partial pressures 131 Gibbs-Dalton 133
Hess 335
of mass action 132
Le Chatelier-Braun principle 175 Le Chatelier’s principle 173 Legendre transformations 63-67 Linear dilatations 221
Liquid
mixtures, standard states of chemical potentials of 136
Liquid (contd.)
state, homogeneous solution re actions 136, 137
Magnetic field,
enthalpy of body in 268 fundamental equation of body in
268
Gibbs free energy of body in 269
Helmholtz free energy of body in 268
quasi-static work done on system in 268
permeability 265
substances—see Diamagnetic sub stances and Paramagnetic sub stances
susceptibility 267 Magnetization,
adiabatic demagnetization 270 density 267
total 268 Magnetocaloric effect 270
Magnetostatic work 265-267 Mass action,
law of 132
equilibrium constants of 132 Massieu-Planck functions 83 Mathematical description of small
deformations 217 Maxwell relations 71, 93, 230
Mechanical stability condition 166 Membrane
equilibria 111-113 non-osmotic 293
of electrolyte solutions 292-295 osmotic 293-295
potential 293, 295, 303 Metastable equilibrium 160 Miscibility gap, closed 180 Molality 136
Molar heat
capacity—see Heat capacity Molarity 136
Molar quantities 73 mean, of state 103 partial 103
Molecular weight 316 determination 315-322 thermodynamic definition 317
Mole fractions 102 of electrolyte 287
mean 287 stoichiometric 287
Motion, perpetual, first kind 8 second kind 9
Multivariant equilibria 124-127
Nernst heat theorem 148,304,338, 340 Planck’s formulation 156
Non-static
change of state 20
processes, Second law applied to 41-45
Onsager type of transition 198 Order, degree of long-range 202 Order-disorder transitions— see
Transitions Osmotic
coefficient 288 equilibrium 112, 293-295 pressure 113, 295
of binary solution 317
Paramagnetic substances 269 Parameters,
conjugate 76 extensive 49, 68 intensive 49, 68, 76 internal 53
Partial
derivatives, conversion 94-102 pressures 131
Dalton’s law of 131 Pfaff
differential equation 26 differentials 25-30
Phase 7, 308—see also Critical phase solid mixed, activity coefficients
137, 139
Phase
reaction 115
rule in chemical reactions 140
Piezo-electricity 252 Poisson’s ratio 234 Polarization,
density 241 total 244
Potential—see also Chemical potential
electrochemical 283 grand 82
membrane 293, 295, 303 single electrode 286, 303
Pressure— see Osmotic pressure, Partial pressure and Vapour pressure
Progress variable 47, 53, 141, 299 Pyroelectric
crystals 254 effect 254
Quadruple points 119 Quasi-static
change of state 20
processes, Second Law applied to 30-35
work—see Work
Reaction isochore 135 Refrigerator 17 Retrograde
condensation 191 vaporization 191
Rotation transitions—see Transitions
Second Law of thermodynamics—see Thermodynamics
Second-order transitions—see Transi tions
Sedimentation equilibrium, equations for 312
in centrifugal field 313 Single electrode potential 286 Solids,
crystalline, ferroelectric 255 pyroelectric 254 vapour pressure 337
free energy, Gibbs 230
Solids (contd.)
free energy {contd.)
Helmholtz
230
fundamental equation
228
Gibbs-Duhem equation 229
stability conditions
236
symmetry properties 231-237
thermal equation of state
229
Solid solutions
activity coefficients
305
Solution,
binary, osmotic pressure
317
ideal dilute
137
Solution point, upper critical 179
Solvent,
activity coefficient 285
elevation of the boiling point
319-
322
lowering,
of the freezing point
322
of the vapour pressure
318, 319
Spinodal curve
185
Stability
conditions
61,
62,
89,
90,
207,
208
for heterogeneous
systems
171—
173
for solids
236
in energy representation 165
mechanical
166
thermal
165
transformation 85-90, 166-171
of chemical equilibria
176, 177
Standard
electrode—see Electrode
state,
for enthalpy
155
for entropy
156
of chemical potentials of liquid
mixtures
136
State 5—see
also
Corresponding
state, Equations of state and
Standard state
change of
20
non-static
20
quasi-static
20
thermal equation
22, 229, 316
variable of
6
Stoichiometric coefficient
46
Strain
coefficients, thermal 340 ellipsoid 220
tensor 220 Stress
coefficients, thermal 340 ellipsoid 224
tensor 224 Stresses,
normal 224 rectangular 224 tangential 224
Superconduction 272-278 Susceptibility,
electrical 242 magnetic 267
Svedberg’s formula 314 System 5, 6
binary 7 closed 6
heterogeneous 7 homogeneous 7 independent components 7 isolated 7
open 7 simple 8 ternary 7
Tangent method 106 Temperature,
absolute 33
Thomson’s definition 12 critical 178
dependence,
of e.m.f. 304
of heat of reaction, differential equations for 335
empirical 22
very low, measurement of 39-41 Thermal
equation of state 22 for solids 229
of one-component gas 316 equilibrium 21
expansion coefficient 95 processes 19
stability condition 165 strain coefficients 340 stress coefficients 340
Thermodynamic
calculation of chemical reactions 141-144
coefficients 205
definition of molecular weight 317 degrees of freedom 114 equilibrium 52
for galvanic cell 297 moduli 204
potentials 76 Thermodynamics,
First Law 8, 9, 23-25 Second Law 9-17
applied to non-static processes 41-45
applied to quasi-static processes 30-35
general formulation 50 Thomson’s principle 9 Tisza’s theory
of critical points and higher-order transitions 208-215
Transition points electric 195 magnetic 195
Л-Transition of helium 194, 199 Transitions,
displacive 214 first-order 195 higher order 194
and critical points, Tisza’s theory 208-215
hyperstructure 194, 201, 215 Onsager type 198 order-disorder 213
rotation 195
second order 197, 277 Ehrenfest equations 198, 277
Triple points 119
Ultracentrifuge 315
Univariant equilibrium 120
van der Waals’ equation of state 324
van’t Hoff equation 135 Vapour pressure
constant 337
Vapour pressure (contd .)
diagram, isothermal, differential equations 333
equation 333
equilibrium, o f aqueous solution of
binary electrolyte
290
o f crystalline solid
337
o f solvent, lowering of
318, 319
saturation,
molar
heat capacities
333
Virial
coefficients
317
equations
317
Virtual displacement
56
Wall,
adiabatic 20
diathermic
20
heat conducting 20
Work coefficient 46
co-ordinates 46, 216 Work,
electrostatic 238-242 magnetostatic 265-267 quasi-static
done on, deformable body 228 material system in electric
field 242
system in magnetic field 268 in electric field 244
in infinitesimal deformation 226 Wrewsky’s theorem 334
Young’s modulus 234
Zero point entropy, conventional 156 Zero, unattainability o f absolute 150
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