Virial equation of state

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The virial equation of state is used to describe the behavior of diluted gases. It is usually written as an expansion of the compressibility factor, , in terms of either the density or the pressure. Such an expansion was first introduced by Kammerlingh Onnes. In the first case:

.

where

  • is the pressure
  • is the volume
  • is the number of molecules
  • is the (number) density
  • is called the k-th virial coefficient

Virial coefficients

The second virial coefficient represents the initial departure from ideal-gas behavior

where is Avogadros number and and are volume elements of two different molecules in configuration space.

One can write the third virial coefficient as

where f is the Mayer f-function (see also: Cluster integrals).

Convergence

See Ref. 3.

References

  1. H. Kammerlingh Onnes "", Communications from the Physical Laboratory Leiden 71 (1901)
  2. James A Beattie and Walter H Stockmayer "Equations of state", Reports on Progress in Physics 7 pp. 195-229 (1940)
  3. J. L. Lebowitz and O. Penrose "Convergence of Virial Expansions", Journal of Mathematical Physics 5 pp. 841-847 (1964)