Equations of state: Difference between revisions
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'''Equations of state''' are generally expressions that relate the macroscopic observables [[pressure]], <math>p</math>, volume, <math>V</math>, and [[temperature]], <math>T</math>. | '''Equations of state''' are generally expressions that relate the macroscopic observables, or ''state variables'', such as [[pressure]], <math>p</math>, volume, <math>V</math>, and [[temperature]], <math>T</math>. | ||
==General== | ==General== | ||
*[[Common bulk modulus point]] | *[[Common bulk modulus point]] | ||
| Line 12: | Line 12: | ||
*[[Second virial coefficient]] | *[[Second virial coefficient]] | ||
*[[Virial coefficients of model systems]] | *[[Virial coefficients of model systems]] | ||
== | ==Semi-empirical equations of state== | ||
Naturally there is the [[Equation of State: Ideal Gas|ideal gas equation of state]]. However, one of the first steps towards a description of realistic substances was the famous [[van der Waals equation of state]]. Since then a plethora of semi-empirical equations have been developed, often in a similar vein to the van der Waals equation of state, each trying to better reproduce the foibles of the many | |||
gasses and/or liquids that are often of industrial interest. | |||
{{columns-list|3| | {{columns-list|3| | ||
*[[Amagat equation of state | Amagat]] | *[[Amagat equation of state | Amagat]] | ||
| Line 30: | Line 32: | ||
*[[Goebel equation of state | Goebel]] | *[[Goebel equation of state | Goebel]] | ||
*[[Hirn equation of state |Hirn]] | *[[Hirn equation of state |Hirn]] | ||
*[[Jäger equation of state | Jäger]] | *[[Jäger equation of state | Jäger]] | ||
*[[Kam equation of state | Kam]] | *[[Kam equation of state | Kam]] | ||
Revision as of 11:59, 23 September 2010
Equations of state are generally expressions that relate the macroscopic observables, or state variables, such as pressure, , volume, , and temperature, .
General
- Common bulk modulus point
- Law of corresponding states
- Linear isothermal regularity
- Maxwell's equal area construction
- Tait-Murnaghan relation
- Zeno line
Virial equations of state
Semi-empirical equations of state
Naturally there is the ideal gas equation of state. However, one of the first steps towards a description of realistic substances was the famous van der Waals equation of state. Since then a plethora of semi-empirical equations have been developed, often in a similar vein to the van der Waals equation of state, each trying to better reproduce the foibles of the many gasses and/or liquids that are often of industrial interest.
- Amagat
- Antoine
- Battelli
- Beattie-Bridgeman
- Benedict, Webb and Rubin
- Berthelot
- Boltzmann
- Boynton and Bramley
- Brillouin
- Clausius
- Dieterici
- Dupré
- Elliott, Suresh, and Donohue
- Fouché
- Goebel
- Hirn
- Jäger
- Kam
- Lagrange
- Leduc
- Linear isothermal regularity
- Lorenz
- Mie
- Murnaghan
- Natanson
- Onnes
- Peczalski
- Peng and Robinson
- Planck
- Porter
- Rankine
- Recknagel
- Redlich-Kwong
- Reinganum
- Sarrau
- Schiller
- Schrieber
- Smoluchowski
- Starkweather
- Tait
- Thiesen
- Tumlirz
- van der Waals
- Walter
- Wohl
- Water equation of state
Other methods
Model systems
Equations of state for idealised models:
- Three-dimensional hard dumbbells
- Hard convex bodies
- Hard rods
- Gaussian overlap model
- Square shoulder model
- Square well model
- Triangular well model
- Equations of state for hard spheres
- Equations of state for crystals of hard spheres
- Equations of state for hard sphere mixtures
- Equations of state for hard disks
- Hard ellipsoid equation of state
- Lennard-Jones equation of state
- Fused hard sphere chains
- Tetrahedral hard sphere model
Interesting reading
- James A. Beattie and Walter H. Stockmayer "Equations of state", Reports on Progress in Physics 7 pp. 195-229 (1940)
- K. K. Shah and G. Thodos "A Comparison of Equations of State", Industrial & Engineering Chemistry 57 pp. 30-37 (1965)
- J. S. Rowlinson "The equation of state of dense systems", Reports on Progress in Physics 28 pp. 169-199 (1965)
Books
- "Equations of State for Fluids and Fluid Mixtures", Eds. J. V. Sengers, R. F. Kayser, C. J. Peters, and H. J. White Jr., Elsevier (2000) ISBN 0-444-50384-6