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
Appendix E - Thermodynamic parameters and derivative relationships
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
Tables E.2 and E.3 present a compact summary of thermodynamic derivatives in a form convenient for geophysical applications. Individual entries have no meaning; they must be taken in pairs so that, for example, to find (∂T/∂P)S look down the constant S column and take the ratio of entries for ∂T and ∂P, that is γT/KS. An arbitrary mass m of material is assumed, so that m appears in many of the entries. Table E.2 is complete for the eight primary parameters. Any one of them may be differentiated with respect to any other one with any third one held constant. The results are represented in terms of the same parameters plus a set of first derivative properties, α, KT, KS, CV, CP and γ. Table E.3 extends the constant T, P, V and S columns to derivatives of these first derivative properties, using a set of second derivative parameters, K′T, K′S, δT, δS, C′T, C′S and q, defined in Table E.1. There are numerous alternative forms for many of the Table E.3 entries, the usefulness of which depends on particular applications. Substitutions may be made using relationships in Table E.4. A few derivatives of products and third derivatives have been found useful and are also listed.
The compact collection of thermodynamic derivatives in Tables E.2 and E.3 follows an idea, started by Bridgman (1914), that is much more useful than generally realized.
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- Information
- Physics of the Earth , pp. 464 - 468Publisher: Cambridge University PressPrint publication year: 2008