Shalom Eliezer, Ajooy Ghatak, Heinrich Hora, Edward Teller9789810248338, 9810248334
Table of contents :
CONTENTS……Page 6
Foreword……Page 12
Preface……Page 14
Preface to the Original Edition……Page 18
1.1 General remarks……Page 20
1.2 Phenomena at various densities and temperatures……Page 21
1.3 Quantum pressure and compressibility……Page 25
1.4 Pressure-temperature diagram……Page 27
1.5 Radiation effects……Page 30
2.1 Phenomenology……Page 34
2.2 Statistical picture……Page 40
2.3 Maxwell-Boltzmann distribution……Page 42
3.1 The partition function……Page 47
3.2 Thermodynamic functions……Page 49
3.3 The Gibbs’ paradox……Page 50
4.1 Classical considerations……Page 53
4.2 The partition function……Page 59
4.3 The vibrational partition function……Page 61
4.4 The rotational partition function……Page 63
4.6 Summary……Page 66
5.1 Introduction……Page 68
5.2 Classical statistics……Page 69
5.3 Bose-Einstein statistics without restriction on the total number of particles: photons……Page 70
5.4 Bose-Einstein statistics for a constant number of particles……Page 74
5.4.1 Bose-Einstein condensation……Page 81
6.2 The grand partition function and other thermodynamic functions……Page 85
6.2.1 The Fermi-Dirac distribution function……Page 88
6.3 Relativistic considerations……Page 95
6.4.1 Non-relativistic case……Page 102
6.4.2 Extreme relativistic case……Page 103
7.2 The thermodynamic formulation……Page 105
7.3 The Saha ionisation formula……Page 108
8.1 Introduction……Page 115
8.2 Charged particle description……Page 116
8.3 Electrostatic energy……Page 118
8.4 Total free energy and equation of state……Page 120
9.1 Overview……Page 123
9.2 The Thomas-Fermi model at T = 0……Page 124
9.2.1 Consideration of a gas of atoms……Page 127
9.2.2 Solution of the Thomas-Fermi equation……Page 128
9.2.3 Derivation of the Thomas-Fermi equation using variational principle……Page 139
9.2.4 The kinetic and potential energies of an atom……Page 140
9.2.5 Calculation of pressure……Page 147
9.3 Inclusion of exchange interaction: the Thomas-Fermi-Dirac equation……Page 151
9.3.1 Calculation of pressure……Page 155
9.4 Derivation of equation (9.103) using the virial theorem……Page 158
9.5 The Thomas-Fermi model at finite temperatures……Page 160
9.5.1 Calculation of thermodynamic functions……Page 163
9.6 Exchange and quantum corrections to the Thomas-Fermi model……Page 168
10.1 Introduction……Page 172
10.2 The Einstein model of solids……Page 174
10.3 The Debye model of solids……Page 176
10.4 The Gruneisen relation……Page 179
10.5 Slater-Landau calculation of y……Page 180
10.6 Results and discussion……Page 183
11.1.1 Mass conservation equation……Page 184
11.1.2 Momentum conservation equation……Page 185
11.1.3 Energy conservation equation……Page 186
11.2 Sound waves and Rieman invariants……Page 188
11.3 Rarefaction waves……Page 192
11.4 Shock waves and the Hugoniot relation……Page 195
12.1 Foundations of hydromechanics……Page 203
12.2 Distribution functions and the Boltzmann equation……Page 204
12.3 Loss of information……Page 208
12.4 Derivation of macroscopic equations……Page 209
12.4.2 The equation of motion (momentum conservation)……Page 210
13.1 Introduction……Page 216
13.2 The Gruneisen coefficient y(V) and an equation for the cold pressure Pc……Page 219
13.3 The specific volume V0c of the ‘zero point’ and the initial conditions for the Pc equation……Page 223
13.4 Isentropic processes near the Hugoniot curve and the free surface velocity……Page 227
13.5 Equations of state for aluminum copper and lead……Page 229
13.6 Semi-empirical interpolation equation of state……Page 236
14.1 Pellet fusion……Page 240
14.2 The limiting case of isentropic (shock-free) volume ignition (selfsimilarity model)……Page 242
14.3 Central core ignition with minimized entropy production……Page 251
14.4.1 The nonlinear-force pushing……Page 261
14.4.2 The cannon ball scheme……Page 263
14.5 The two-temperature equation of state……Page 265
14.5.1 Electronic contributions to the EOS……Page 266
14.5.2 The ion contributions to the EOS……Page 267
14.5.3 Results and discussion……Page 274
15.1 Overview……Page 276
15.1.1 The equation of state for an ideal gas……Page 278
15.1.2 The equation of state for a degenerate electron gas……Page 281
15.2 The equation of hydrostatic equilibrium……Page 286
15.3 Expressions for pressure and temperature inside a star……Page 288
15.4 Numerical estimates of Pc P and T by assuming uniform density inside the star……Page 291
15.5 Some useful theorems……Page 292
15.6.1 The gravitational potential energy……Page 293
15.6.2 The virial theorem……Page 294
15.7 Qualitative understanding of the evolution of a star……Page 298
15.8 The contribution due to radiation pressure……Page 302
15.9 The polytropic model……Page 305
15.10 The standard model……Page 313
15.11 The white dwarf stars……Page 318
15.11.1 Solution of the equation of hydrostatic equilibrium for a completely degenerate gas in the extreme relativistic limit……Page 319
15.11.2 The general solution corresponding to a completely degenerate gas……Page 320
16.1 Overview……Page 324
16.2.1 Introduction……Page 325
16.2.2 The partition function……Page 327
16.2.3 The bootstrap condition……Page 329
16.2.4 The thermodynamic functions: pressure and energy……Page 334
16.2.5 Transverse momentum distribution……Page 336
1 A free particle inside a box and the density of states……Page 340
2 The Stirling formula……Page 344
3 Table of Fermi-Dirac functions……Page 345
4 Derivation of the virial theorem result……Page 352
5 Tables of Thomas-Fermi corrected equation of state……Page 356
6 Some mathematical relations for Chapter 13……Page 370
7 A note on the Lawson criterion……Page 372
8 Derivation of the equation describing hydrostatic equilibrium for a completely degenerate gas……Page 373
References……Page 374
Index……Page 381
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