Virial equation of state: Difference between revisions

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


:<math>B_{2}(T)= \frac{N_0}{2V} \int .... \int (1-e^{-\Phi/k_BT}) ~d\tau_1 d\tau_2</math>
:<math>B_{2}(T)= \frac{N_A}{2V} \int .... \int (1-e^{-\Phi/k_BT}) ~d\tau_1 d\tau_2</math>


where <math>N_0</math> is [[Avogadro constant | Avogadros number]] and <math>d\tau_1</math> and <math>d\tau_2</math> are volume elements of two different molecules
where <math>N_A</math> is [[Avogadro constant | Avogadros number]] and <math>d\tau_1</math> and <math>d\tau_2</math> are volume elements of two different molecules
in configuration space.  
in configuration space.  



Revision as of 13:54, 19 February 2008

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). See also:

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)