Book contents
- Frontmatter
- Contents
- Preface
- 1 Origin and history of the Solar System
- 2 Composition of the Earth
- 3 Radioactivity, isotopes and dating
- 4 Isotopic clues to the age and origin of the Solar System
- 5 Evidence of the Earth's evolutionary history
- 6 Rotation, figure of the Earth and gravity
- 7 Precession, wobble and rotational irregularities
- 8 Tides and the evolution of the lunar orbit
- 9 The satellite geoid, isostasy, post-glacial rebound and mantle viscosity
- 10 Elastic and inelastic properties
- 11 Deformation of the crust: rock mechanics
- 12 Tectonics
- 13 Convective and tectonic stresses
- 14 Kinematics of the earthquake process
- 15 Earthquake dynamics
- 16 Seismic wave propagation
- 17 Seismological determination of Earth structure
- 18 Finite strain and high-pressure equations of state
- 19 Thermal properties
- 20 The surface heat flux
- 21 The global energy budget
- 22 Thermodynamics of convection
- 23 Thermal history
- 24 The geomagnetic field
- 25 Rock magnetism and paleomagnetism
- 26 ‘Alternative’ energy sources and natural climate variations: some geophysical background
- Appendix A General reference data
- Appendix B Orbital dynamics (Kepler's laws)
- Appendix C Spherical harmonic functions
- Appendix D Relationships between elastic moduli of an isotropic solid
- Appendix E Thermodynamic parameters and derivative relationships
- Appendix F An Earth model: mechanical properties
- Appendix G A thermal model of the Earth
- Appendix H Radioactive isotopes
- Appendix I A geologic time scale
- Appendix J Problems
- References
- Name Index
- Subject Index
18 - Finite strain and high-pressure equations of state
Published online by Cambridge University Press: 05 July 2013
- Frontmatter
- Contents
- Preface
- 1 Origin and history of the Solar System
- 2 Composition of the Earth
- 3 Radioactivity, isotopes and dating
- 4 Isotopic clues to the age and origin of the Solar System
- 5 Evidence of the Earth's evolutionary history
- 6 Rotation, figure of the Earth and gravity
- 7 Precession, wobble and rotational irregularities
- 8 Tides and the evolution of the lunar orbit
- 9 The satellite geoid, isostasy, post-glacial rebound and mantle viscosity
- 10 Elastic and inelastic properties
- 11 Deformation of the crust: rock mechanics
- 12 Tectonics
- 13 Convective and tectonic stresses
- 14 Kinematics of the earthquake process
- 15 Earthquake dynamics
- 16 Seismic wave propagation
- 17 Seismological determination of Earth structure
- 18 Finite strain and high-pressure equations of state
- 19 Thermal properties
- 20 The surface heat flux
- 21 The global energy budget
- 22 Thermodynamics of convection
- 23 Thermal history
- 24 The geomagnetic field
- 25 Rock magnetism and paleomagnetism
- 26 ‘Alternative’ energy sources and natural climate variations: some geophysical background
- Appendix A General reference data
- Appendix B Orbital dynamics (Kepler's laws)
- Appendix C Spherical harmonic functions
- Appendix D Relationships between elastic moduli of an isotropic solid
- Appendix E Thermodynamic parameters and derivative relationships
- Appendix F An Earth model: mechanical properties
- Appendix G A thermal model of the Earth
- Appendix H Radioactive isotopes
- Appendix I A geologic time scale
- Appendix J Problems
- References
- Name Index
- Subject Index
Summary
Preamble
An equation of state is a relationship between volume, V, pressure, P, and temperature, T, of a specified mass of material. If density, ρ, is used instead of V then specification of mass is unnecessary, and in some treatments V is specific volume, 1/ρ, but in this text V is the volume of an arbitrary mass, m. Another alternative is molar volume, but moles can be inconvenient units for materials with non-integral proportions of different elements. The simplest and most familiar equation of state is the ideal gas equation for n moles of gas, PV = nRT, where R = NAk = 8.314 47 J mol− 1 K− 1 is the gas constant and is related to Boltzmann's constant, k = 1.380 65 × 10− 23 JK− 1 by Avogadro's number, NA = 6.022 14 × 1023 mol− 1. It is an example of a complete equation of state, by which is meant one representing V as a function of both P and T, not that it gives all of the properties. In dealing with condensed matter (solids and liquids) it is generally convenient to consider the P and T effects separately. Compression at constant T is described by the isothermal bulk modulus or incompressibility, KT = − V(∂P/∂V)T. This is a parameter of elasticity theory (Chapter 10), which is restricted to small strains, that is, for volume compression, P/KT = −ΔV/V ≪ 1.
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- Physics of the Earth , pp. 294 - 313Publisher: Cambridge University PressPrint publication year: 2008
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