Fundamentals of Equations of State.
Başlık:
Fundamentals of Equations of State.
Yazar:
Eliezer, Shalom.
ISBN:
9789812778130
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 online resource (386 pages)
İçerik:
CONTENTS -- Foreword -- Preface -- Preface to the Original Edition -- 1 Introduction -- 1.1 General remarks -- 1.2 Phenomena at various densities and temperatures -- 1.3 Quantum pressure and compressibility -- 1.4 Pressure-temperature diagram -- 1.5 Radiation effects -- 2 A summary of thermodynamics -- 2.1 Phenomenology -- 2.2 Statistical picture -- 2.3 Maxwell-Boltzmann distribution -- 3 Equation of state for an ideal gas -- 3.1 The partition function -- 3.2 Thermodynamic functions -- 3.3 The Gibbs' paradox -- 4 Law of equipartition of energy and effects of vibrational and rotational motions -- 4.1 Classical considerations -- 4.2 The partition function -- 4.3 The vibrational partition function -- 4.4 The rotational partition function -- 4.5 The electronic partition function -- 4.6 Summary -- 5 Bose-Einstein equation of state -- 5.1 Introduction -- 5.2 Classical statistics -- 5.3 Bose-Einstein statistics without restriction on the total number of particles: photons -- 5.4 Bose-Einstein statistics for a constant number of particles -- 5.4.1 Bose-Einstein condensation -- 6 Fermi Dirac equation of state -- 6.1 Overview -- 6.2 The grand partition function and other thermodynamic functions -- 6.2.1 The Fermi-Dirac distribution function -- 6.3 Relativistic considerations -- 6.4 Adiabatic processes -- 6.4.1 Non-relativistic case -- 6.4.2 Extreme relativistic case -- 7 Ionization equilibrium and the Saha equation -- 7.1 Introduction -- 7.2 The thermodynamic formulation -- 7.3 The Saha ionisation formula -- 8 Debye-Huckel equation of state -- 8.1 Introduction -- 8.2 Charged particle description -- 8.3 Electrostatic energy -- 8.4 Total free energy and equation of state -- 9 The Thomas-Fermi and related models -- 9.1 Overview -- 9.2 The Thomas-Fermi model at T = 0 -- 9.2.1 Consideration of a gas of atoms.
9.2.2 Solution of the Thomas-Fermi equation -- 9.2.3 Derivation of the Thomas-Fermi equation using variational principle -- 9.2.4 The kinetic and potential energies of an atom -- 9.2.5 Calculation of pressure -- 9.3 Inclusion of exchange interaction: the Thomas-Fermi-Dirac equation -- 9.3.1 Calculation of pressure -- 9.4 Derivation of equation (9.103) using the virial theorem -- 9.5 The Thomas-Fermi model at finite temperatures -- 9.5.1 Calculation of thermodynamic functions -- 9.6 Exchange and quantum corrections to the Thomas-Fermi model -- 10 Gruneisen equation of state -- 10.1 Introduction -- 10.2 The Einstein model of solids -- 10.3 The Debye model of solids -- 10.4 The Gruneisen relation -- 10.5 Slater-Landau calculation of y -- 10.6 Results and discussion -- 11 An introduction to fluid mechanics in relation to shock waves -- 11.1 Fluid equations of motion -- 11.1.1 Mass conservation equation -- 11.1.2 Momentum conservation equation -- 11.1.3 Energy conservation equation -- 11.2 Sound waves and Rieman invariants -- 11.3 Rarefaction waves -- 11.4 Shock waves and the Hugoniot relation -- 12 Derivation of hydrodynamics from kinetic theory -- 12.1 Foundations of hydromechanics -- 12.2 Distribution functions and the Boltzmann equation -- 12.3 Loss of information -- 12.4 Derivation of macroscopic equations -- 12.4.1 The equation of continuity (mass conservation) -- 12.4.2 The equation of motion (momentum conservation) -- 13 Studies of the equations of state from high pressure shock waves in solids -- 13.1 Introduction -- 13.2 The Gruneisen coefficient y(V) and an equation for the cold pressure Pc -- 13.3 The specific volume V0c of the 'zero point' and the initial conditions for the Pc equation.
13.4 Isentropic processes near the Hugoniot curve and the free surface velocity -- 13.5 Equations of state for aluminum copper and lead -- 13.6 Semi-empirical interpolation equation of state -- 14 Equation of state and inertial confinement fusion -- 14.1 Pellet fusion -- 14.2 The limiting case of isentropic (shock-free) volume ignition (selfsimilarity model) -- 14.3 Central core ignition with minimized entropy production -- 14.4 Alternative driving schemes: nonlinear force cannon ball -- 14.4.1 The nonlinear-force pushing -- 14.4.2 The cannon ball scheme -- 14.5 The two-temperature equation of state -- 14.5.1 Electronic contributions to the EOS -- 14.5.2 The ion contributions to the EOS -- 14.5.3 Results and discussion -- 15 Applications of equations of state in astrophysics -- 15.1 Overview -- 15.1.1 The equation of state for an ideal gas -- 15.1.2 The equation of state for a degenerate electron gas -- 15.1.3 The radiation pressure -- 15.2 The equation of hydrostatic equilibrium -- 15.3 Expressions for pressure and temperature inside a star -- 15.4 Numerical estimates of Pc P and T by assuming uniform density inside the star -- 15.5 Some useful theorems -- 15.6 The gravitational potential energy and the virial theorem -- 15.6.1 The gravitational potential energy -- 15.6.2 The virial theorem -- 15.7 Qualitative understanding of the evolution of a star -- 15.8 The contribution due to radiation pressure -- 15.9 The polytropic model -- 15.10 The standard model -- 15.11 The white dwarf stars -- 15.11.1 Solution of the equation of hydrostatic equilibrium for a completely degenerate gas in the extreme relativistic limit -- 15.11.2 The general solution corresponding to a completely degenerate gas -- 16 Equations of state in elementary particle physics -- 16.1 Overview.
16.2 Hagedorn model of strong interactions -- 16.2.1 Introduction -- 16.2.2 The partition function -- 16.2.3 The bootstrap condition -- 16.2.4 The thermodynamic functions: pressure and energy -- 16.2.5 Transverse momentum distribution -- Appendixes -- 1 A free particle inside a box and the density of states -- 2 The Stirling formula -- 3 Table of Fermi-Dirac functions -- 4 Derivation of the virial theorem result -- 5 Tables of Thomas-Fermi corrected equation of state -- 6 Some mathematical relations for Chapter 13 -- 7 A note on the Lawson criterion -- 8 Derivation of the equation describing hydrostatic equilibrium for a completely degenerate gas -- References -- Index.
Özet:
The equation of state was originally developed for ideal gases, and proved central to the development of early molecular and atomic physics. Increasingly sophisticated equations of state have been developed to take into account molecular interactions, quantization, relativistic effects, etc. Extreme conditions of matter are encountered both in nature and in the laboratory, for example in the centres of stars, in relativistic collisions of heavy nuclei, in inertial confinement fusion (where a temperature of 10 9 K and a pressure exceeding a billion atmospheres can be achieved). A sound knowledge of the equation of state is a prerequisite for understanding processes at very high temperatures and pressures, as noted in some recent developments. This book 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. Contents: A Summary of Thermodynamics; Equation of State for an Ideal Gas; Law of Equipartition of Energy and Effects of Vibrational and Rotational Motions; Bose-Einstein Equation of State; Fermi-Dirac Equation of State; Ionization Equilibrium and the Saha Equation; Debye-Hückel Equation of State; The Thomas-Fermi and Related Models; Grüneisen Equation of State; An Introduction to Fluid Mechanics in Relation to Shock Waves; Derivation of Hydrodynamics from Kinetic Theory; Studies of the Equations of State from High Pressure Shock Waves in Solids; Equation of State and Inertial Confinement Fusion; Applications of Equations of State in Astrophysics; Equations of State in Elementary Particle Physics. Readership: Upper level undergraduates, graduate students, researchers and academics in theoretical physics, theoretical and nuclear chemistry, materials and mechanical engineering.
Notlar:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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