# Equations of state

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

## Contents

## 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
- Cole
- 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

# See also=

## 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