Fundamentals of Equations of State

by Eliezer, Shalom; Ghatak, A. K.; Hora, Heinrich; Teller, Edward

• ISBN13: 9789810248338
• ISBN10: 9810248334
• Format: Hardcover
• Copyright: 2002-05-01
• Publisher: World Scientific Pub Co Inc

Summary

Presents a detailed pedagogical account of the equation of state and its applications in several important and fast-growing topics in theoretical physics, chemistry and engineering.

Table of Contents

Foreword	p. xi
Preface	p. xiii
Preface to the Original Edition	p. xvii
Introduction	p. 1
General remarks	p. 1
Phenomena at various densities and temperatures	p. 2
Quantum pressure and compressibility	p. 6
Pressure-temperature diagram	p. 8
Radiation effects	p. 11
A summary of thermodynamics	p. 15
Phenomenology	p. 15
Statistical picture	p. 21
Maxwell-Boltzmann distribution	p. 23
Equation of state for an ideal gas	p. 28
The partition function	p. 28
Thermodynamic functions	p. 30
The Gibbs' paradox	p. 31
Law of equipartition of energy and effects of vibrational and rotational motions	p. 34
Classical considerations	p. 34
The partition function	p. 40
The vibrational partition function	p. 42
The rotational partition function	p. 44
The electronic partition function	p. 47
Summary	p. 47
Bose-Einstein equation of state	p. 49
Introduction	p. 49
Classical statistics	p. 50
Bose-Einstein statistics without restriction on the total number of particles: photons	p. 51
Bose-Einstein statistics for a constant number of particles	p. 55
Bose-Einstein condensation	p. 62
Fermi-Dirac equation of state	p. 66
Overview	p. 66
The grand partition function and other thermodynamic functions	p. 66
The Fermi-Dirac distribution function	p. 69
Relativistic considerations	p. 76
Adiabatic processes	p. 83
Non-relativistic case	p. 83
Extreme relativistic case	p. 84
Ionization equilibrium and the Saha equation	p. 86
Introduction	p. 86
The thermodynamic formulation	p. 86
The Saha ionisation formula	p. 89
Debye-Huckel equation of state	p. 96
Introduction	p. 96
Charged particle description	p. 97
Electrostatic energy	p. 99
Total free energy and equation of state	p. 101
The Thomas-Fermi and related models	p. 104
Overview	p. 104
The Thomas-Fermi model at T = 0	p. 105
Consideration of a gas of atoms	p. 108
Solution of the Thomas-Fermi equation	p. 109
Derivation of the Thomas-Fermi equation using variational principle	p. 120
The kinetic and potential energies of an atom	p. 121
Calculation of pressure	p. 128
Inclusion of exchange interaction: the Thomas-Fermi-Dirac equation	p. 132
Calculation of pressure	p. 136
Derivation of equation (9.103) using the virial theorem	p. 139
The Thomas-Fermi model at finite temperatures	p. 141
Calculation of thermodynamic functions	p. 144
Exchange and quantum corrections to the Thomas-Fermi model	p. 149
Gruneisen equation of state	p. 153
Introduction	p. 153
The Einstein model of solids	p. 155
The Debye model of solids	p. 157
The Gruneisen relation	p. 160
Slater-Landau calculation of [gamma]	p. 161
Results and discussion	p. 164
An introduction to fluid mechanics in relation to shock waves	p. 165
Fluid equations of motion	p. 165
Mass conservation equation	p. 165
Momentum conservation equation	p. 166
Energy conservation equation	p. 167
Sound waves and Rieman invariants	p. 169
Rarefaction waves	p. 173
Shock waves and the Hugoniot relation	p. 176
Derivation of hydrodynamics from kinetic theory	p. 184
Foundations of hydromechanics	p. 184
Distribution functions and the Boltzmann equation	p. 185
Loss of information	p. 189
Derivation of macroscopic equations	p. 190
The equation of continuity (mass conservation)	p. 191
The equation of motion (momentum conservation)	p. 191
Studies of the equations of state from high pressure shock waves in solids	p. 197
Introduction	p. 197
The Gruneisen coefficient [gamma](V) and an equation for the cold pressure P[subscript c]	p. 200
The specific volume V[subscript oc] of the 'zero point' and the initial conditions for the P[subscript c] equation	p. 204
Isentropic processes near the Hugoniot curve and the free surface velocity	p. 208
Equations of state for aluminum, copper and lead	p. 210
Semi-empirical interpolation equation of state	p. 217
Equation of state and inertial confinement fusion	p. 221
Pellet fusion	p. 221
The limiting case of isentropic (shock-free) volume ignition (self-similarity model)	p. 223
Central core ignition with minimized entropy production	p. 232
Alternative driving schemes: nonlinear force, cannon ball	p. 242
The nonlinear-force pushing	p. 242
The cannon ball scheme	p. 244
The two-temperature equation of state	p. 246
Electronic contributions to the EOS	p. 247
The ion contributions to the EOS	p. 248
Results and discussion	p. 255
Applications of equations of state in astrophysics	p. 257
Overview	p. 257
The equation of state for an ideal gas	p. 259
The equation of state for a degenerate electron gas	p. 262
The radiation pressure	p. 267
The equation of hydrostatic equilibrium	p. 267
Expressions for pressure and temperature inside a star	p. 269
Numerical estimates of P[subscript c], P and T by assuming uniform density inside the star	p. 272
Some useful theorems	p. 273
The gravitational potential energy and the virial theorem	p. 274
The gravitational potential energy	p. 274
The virial theorem	p. 275
Qualitative understanding of the evolution of a star	p. 279
The contribution due to radiation pressure	p. 283
The polytropic model	p. 286
The standard model	p. 294
The white dwarf stars	p. 299
Solution of the equation of hydrostatic equilibrium for a completely degenerate gas in the extreme relativistic limit	p. 300
The general solution corresponding to a completely degenerate gas	p. 301
Equations of state in elementary particle physics	p. 305
Overview	p. 305
Hagedorn model of strong interactions	p. 306
Introduction	p. 306
The partition function	p. 308
The bootstrap condition	p. 310
The thermodynamic functions: pressure and energy	p. 315
Transverse momentum distribution	p. 317
Appendixes	p. 321
A free particle inside a box and the density of states	p. 321
The Stirling formula	p. 325
Table of Fermi-Dirac functions	p. 326
Derivation of the virial theorem result	p. 333
Tables of Thomas-Fermi corrected equation of state	p. 337
Some mathematical relations for Chapter 13	p. 351
A note on the Lawson criterion	p. 353
Derivation of the equation describing hydrostatic equilibrium for a completely degenerate gas	p. 354
References	p. 355
Index	p. 362
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