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 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

• 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

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