Equations of state

Equations of state are generally expressions that relate the macroscopic observables, or state variables, such as pressure, $p$, volume, $V$, and temperature, $T$.

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

• Virial equation of state
• Second virial coefficient
• Virial coefficients of model systems

Semi-empirical equations of state

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

• ASOG (Analytical Solution of Groups)
• UNIFAC (Universal Functional Activity Coefficient)

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

See also

• Pair stress approximation
• Scaled-particle theory

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