Fundamentals of Equations of State

The following sections are included:

• ABOUT THE AUTHORS

• CONTENTS

• FOREWORD BY EDWARD TELLER

• PREFACE

• PREFACE TO THE ORIGINAL EDITION

The following sections are included:

• General remarks

• Phenomena at various densities and temperatures

• Quantum pressure and compressibility

• Pressure–temperature diagram

• Radiation effects

The following sections are included:

• Phenomenology

• Statistical picture

• Maxwell–Boltzmann distribution

The following sections are included:

• The partition function

• Thermodynamic functions

• The Gibbs' paradox

The following sections are included:

• Classical considerations

• The partition function

• The vibrational partition function

• The rotational partition function

• The electronic partition function

• Summary

The following sections are included:

• Introduction

• Classical statistics

• Bose–Einstein statistics without restriction on the total number of particles: photons

• Bose–Einstein statistics for a constant number of particles
  • Bose–Einstein condensation

The following sections are included:

• Overview

• The grand partition function and other thermodynamic functions
  • The Fermi–Dirac distribution function

• Relativistic considerations

• Adiabatic processes
  • Non-relativistic case
  • Extreme relativistic case

The following sections are included:

• Introduction

• The thermodynamic formulation

• The Saha ionization formula

The following sections are included:

• Introduction

• Charged particle description

• Electrostatic energy

• Total free energy and equation of state

The following sections are included:

• Overview

• The Thomas–Fermi model at T = 0
  • Consideration of a gas of atoms
  • Solution of the Thomas–Fermi equation
  • Derivation of the Thomas–Fermi equation using variational principle
  • The kinetic and potential energies of an atom
  • Calculation of pressure

• Inclusion of exchange interaction: the Thomas–Fermi–Dirac equation
  • Calculation of pressure

• Derivation of equation (9.103) using the virial theorem

• The Thomas–Fermi model at finite temperatures
  • Calculation of thermodynamic functions

• Exchange and quantum corrections to the Thomas–Fermi model

The following sections are included:

• Introduction

• The Einstein model of solids

• The Debye model of solids

• The Grüneisen relation

• Slater–Landau calculation of γ

• Results and discussion

The following sections are included:

• Fluid equations of motion
  • Mass conservation equation
  • Momentum conservation equation
  • Energy conservation equation

• Sound waves and Rieman invariants

• Rarefaction waves

• Shock waves and the Hugoniot relation

The following sections are included:

• Foundations of hydromechanics

• Distribution functions and the Boltzmann equation

• Loss of information

• Derivation of macroscopic equations
  • The equation of continuity (mass conservation)
  • The equation of motion (momentum conservation)

The following sections are included:

• Introduction

• The Grüneisen coefficient γ(V) and an equation for the cold pressure P_c

• The specific volume V_0c of the 'zero point' and the initial conditions for the P_c equation

• Isentropic processes near the Hugoniot curve and the free surface velocity

• Equations of state for aluminum, copper and lead

• Semi-empirical interpolation equation of state

The following sections are included:

• Pellet fusion

• The limiting case of isentropic (shock-free) volume ignition (self-similarity model)

• Central core ignition with minimized entropy production

• Alternative driving schemes: nonlinear force, cannon ball
  • The nonlinear-force pushing
  • The cannon ball scheme

• The two-temperature equation of state
  • Electronic contributions to the EOS
  • The ion contributions to the EOS
  • Results and discussion

The following sections are included:

• Overview
  • The equation of state for an ideal gas
  • The equation of state for a degenerate electron gas
  • The radiation pressure

• The equation of hydrostatic equilibrium

• Expressions for pressure and temperature inside a star

• Numerical estimates of P_c, and by assuming uniform density inside the star

• Some useful theorems

• The gravitational potential energy and the virial theorem
  • The gravitational potential energy
  • The virial theorem

• Qualitative understanding of the evolution of a star

• The contribution due to radiation pressure

• The polytropic model

• The standard model

• The white dwarf stars
  • Solution of the equation of hydrostatic equilibrium for a completely degenerate gas in the extreme relativistic limit
  • The general solution corresponding to a completely degenerate gas

The following sections are included:

• Overview

• Hagedorn model of strong interactions
  • Introduction
  • The partition function
  • The bootstrap condition
  • The thermodynamic functions: pressure and energy
  • Transverse momentum distribution

The following sections are included:

• APPENDIX 1 A free particle inside a box and the density of states

• APPENDIX 2 The Stirling formula

• APPENDIX 3 Table of Fermi–Dirac functions

• APPENDIX 4 Derivation of the virial theorem result

• APPENDIX 5 Tables of Thomas–Fermi corrected equation of state

• APPENDIX 6 Some mathematical relations for Chapter 13

• APPENDIX 7 A note on the Lawson criterion

• APPENDIX 8 Derivation of the equation describing hydrostatic equilibrium for a completely degenerate gas

• REFERENCES

• INDEX