Equations of state: Difference between revisions
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'''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]] | ||
*[[Law of corresponding states]] | *[[Law of corresponding states]] | ||
*[[Linear isothermal regularity]] | *[[Linear isothermal regularity]] | ||
*[[Maxwell's equal area construction]] | |||
*[[Tait-Murnaghan relation]] | *[[Tait-Murnaghan relation]] | ||
*[[Zeno line]] | *[[Zeno line]] | ||
==Virial equations of state== | ==Virial equations of state== | ||
*[[Virial equation of state]] | *[[Virial equation of state]] | ||
*[[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]]. However, one of the first to describe realistic substances was the famous [[van der Waals equation of state]]. Since then, many semi-empirical equations have been developed, often in a similar vein to the van der Waals equation of state, each trying to give better estimations of the many | |||
gasses and/or liquids that are often of industrial interest. | |||
*[[Beattie-Bridgeman equation of state]] | {{columns-list|3| | ||
*[[Benedict, Webb and Rubin equation of state]] | *[[Amagat equation of state |Amagat]] | ||
*[[Berthelot equation of state]] | *[[Antoine equation of state |Antoine]] | ||
*[[Clausius equation of state]] | *[[Baonza equation of state |Baonza]] | ||
*[[Dieterici equation of state]] | *[[BACK equation of state |BACK]] | ||
*[[Elliott, Suresh, and Donohue equation of state]] | *[[Battelli equation of state |Battelli]] | ||
*[[Beattie-Bridgeman equation of state |Beattie-Bridgeman]] | |||
*[[Benedict, Webb and Rubin equation of state |Benedict, Webb, and Rubin]] | |||
*[[Berthelot equation of state |Berthelot]] | |||
*[[Birch-Murnaghan equation of state |Birch-Murnaghan]] | |||
*[[Boltzmann equation|Boltzmann]] | |||
*[[Boynton and Bramley equation of state |Boynton and Bramley]] | |||
*[[Brillouin equation of state |Brillouin]] | |||
*[[Clausius equation of state |Clausius]] | |||
*[[Cole equation of state |Cole]] | |||
*[[Dalton's law|Dalton]] | |||
*[[BACK equation of state |DIBACK]] | |||
*[[Dieterici equation of state |Dieterici]] | |||
*[[Dupré equation of state |Dupré]] | |||
*[[Elliott, Suresh, and Donohue equation of state |Elliott, Suresh, and Donohue]] | |||
*[[Fouché equation of state |Fouché]] | |||
*[[Goebel equation of state |Goebel]] | |||
*[[Hirn equation of state |Hirn]] | |||
*[[Holzapfel equation of state |Holzapfel]] | |||
*[[Jäger equation of state |Jäger]] | |||
*[[Kam equation of state |Kam]] | |||
*[[Kumari-Dass equation of state |Kumari-Dass]] | |||
*[[Lagrange equation of state |Lagrange]] | |||
*[[Leduc equation of state |Leduc]] | |||
*[[Linear isothermal regularity]] | *[[Linear isothermal regularity]] | ||
*[[Peng and Robinson equation of state]] | *[[Lorentz equation of state |Lorenz]] | ||
*[[Redlich-Kwong equation of state]] | *[[Mie potential|Mie]] | ||
*[[Wohl equation of state]] | *[[BACK equation of state |MOBACK]] | ||
*[[Water equation of state]] | *[[Mohsen-Nia, Modarress and Mansoori equation of state |Mohsen-Nia, Modarress, and Mansoori]] | ||
== | *[[Murnaghan equation of state |Murnaghan]] | ||
*[[Natanson equation of state |Natanson]] | |||
*[[BACK equation of state |NIK]] | |||
*[[Onnes equation of state |Onnes]] | |||
*[[Peczalski equation of state |Peczalski]] | |||
*[[Peng and Robinson equation of state |Peng and Robinson]] | |||
*[[Planck equation of state |Planck]] | |||
*[[Porter equation of state |Porter]] | |||
*[[BACK equation of state |QUABACK]] | |||
*[[Rankine equation of state |Rankine]] | |||
*[[Recknagel equation of state |Recknagel]] | |||
*[[Redlich-Kwong equation of state |Redlich-Kwong]] | |||
*[[Reinganum equation of state |Reinganum]] | |||
*[[Rose-Vinet (Universal) equation of state |Rose-Vinet]] | |||
*[[Sarrau equation of state |Sarrau]] | |||
*[[Schiller equation of state |Schiller]] | |||
*[[Schrieber equation of state |Schrieber]] | |||
*[[Smoluchowski equation|Smoluchowski]] | |||
*[[Starkweather equation of state |Starkweather]] | |||
*[[Stiffened equation of state |Stiffened]] | |||
*[[Tait equation of state |Tait]] | |||
*[[Thiesen equation of state |Thiesen]] | |||
*[[Tillotson equation of state |Tillotson]] | |||
*[[Tumlirz equation of state |Tumlirz]] | |||
*[[Twu-Sim-Tassone equation of state |Twu-Sim-Tassone]] | |||
*[[van der Waals equation of state |van der Waals]] | |||
*[[Walter equation of state |Walter]] | |||
*[[Wohl equation of state |Wohl]] | |||
*[[Phase diagrams of water |Water equation of state]] | |||
}} | |||
==Other methods== | |||
*[[ASOG (Analytical Solution of Groups)]] | |||
*[[UNIFAC (Universal Functional Activity Coefficient)]] | |||
==Model systems== | ==Model systems== | ||
Equations of state for [[idealised models]]: | Equations of state for [[idealised models]]: | ||
| Line 36: | Line 93: | ||
*[[Equations of state for the triangular well model | Triangular well model]] | *[[Equations of state for the triangular well model | Triangular well model]] | ||
*[[Equations of state for hard spheres]] | *[[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 sphere mixtures]] | ||
*[[Equations of state for hard disks]] | *[[Equations of state for hard disks]] | ||
*[[Hard ellipsoid equation of state]] | *[[Hard ellipsoid equation of state]] | ||
*[[Lennard-Jones equation of state]] | *[[Lennard-Jones equation of state]] | ||
*[[Fused hard sphere chains#Equation of state | Fused hard sphere chains]] | |||
*[[Tetrahedral hard sphere model#Equation of state|Tetrahedral hard sphere model]] | |||
==== | ==See also== | ||
*[[Pair stress approximation]] | |||
*[[Scaled-particle theory]] | |||
==Interesting reading== | |||
*[http://dx.doi.org/10.1088/0034-4885/7/1/312 James A. Beattie and Walter H. Stockmayer "Equations of state", Reports on Progress in Physics '''7''' pp. 195-229 (1940)] | |||
*[http://dx.doi.org/10.1021/ie50663a005 K. K. Shah and G. Thodos "A Comparison of Equations of State", Industrial & Engineering Chemistry '''57''' pp. 30-37 (1965)] | |||
*[http://dx.doi.org/10.1088/0034-4885/28/1/306 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 | |||
[[Category: Results]] | |||
Latest revision as of 01:34, 1 June 2021
Equations of state are generally expressions that relate the macroscopic observables, or state variables, such as pressure, , volume, , and temperature, .
General[edit]
- 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[edit]
Semi-empirical equations of state[edit]
Naturally, there is the ideal gas equation. However, one of the first to describe realistic substances was the famous van der Waals equation of state. Since then, many semi-empirical equations have been developed, often in a similar vein to the van der Waals equation of state, each trying to give better estimations of the many gasses and/or liquids that are often of industrial interest.
- Amagat
- Antoine
- Baonza
- BACK
- Battelli
- Beattie-Bridgeman
- Benedict, Webb, and Rubin
- Berthelot
- Birch-Murnaghan
- Boltzmann
- Boynton and Bramley
- Brillouin
- Clausius
- Cole
- Dalton
- DIBACK
- Dieterici
- Dupré
- Elliott, Suresh, and Donohue
- Fouché
- Goebel
- Hirn
- Holzapfel
- Jäger
- Kam
- Kumari-Dass
- Lagrange
- Leduc
- Linear isothermal regularity
- Lorenz
- Mie
- MOBACK
- Mohsen-Nia, Modarress, and Mansoori
- Murnaghan
- Natanson
- NIK
- Onnes
- Peczalski
- Peng and Robinson
- Planck
- Porter
- QUABACK
- Rankine
- Recknagel
- Redlich-Kwong
- Reinganum
- Rose-Vinet
- Sarrau
- Schiller
- Schrieber
- Smoluchowski
- Starkweather
- Stiffened
- Tait
- Thiesen
- Tillotson
- Tumlirz
- Twu-Sim-Tassone
- van der Waals
- Walter
- Wohl
- Water equation of state
Other methods[edit]
Model systems[edit]
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
See also[edit]
Interesting reading[edit]
- 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