Virial equation of state: Difference between revisions

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The '''virial equation of state''' is used to describe the behavior of diluted gases.  
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]], <math> Z </math>, in terms of either the
It is usually written as an expansion of the [[compressibility factor]], <math> Z </math>, in terms of either the
density or the pressure. Such an expansion was first introduced by in 1885 by Thiesen <ref>[http://dx.doi.org/10.1002/andp.18852600308 M. Thiesen "Untersuchungen über die Zustandsgleichung", Annalen der Physik '''24''' pp. 467-492 (1885)]</ref> and extensively studied by Heike Kamerlingh Onnes <ref> H. Kammerlingh Onnes "Expression of the equation of state of gases and liquids by means of series", Communications from the Physical Laboratory of the University of Leiden '''71''' pp. 3-25 (1901)</ref>
density or the pressure. Such an expansion was first introduced in 1885 by Thiesen <ref>[http://dx.doi.org/10.1002/andp.18852600308 M. Thiesen "Untersuchungen über die Zustandsgleichung", Annalen der Physik '''24''' pp. 467-492 (1885)]</ref> and extensively studied by Heike Kamerlingh Onnes <ref> H. Kammerlingh Onnes "Expression of the equation of state of gases and liquids by means of series", Communications from the Physical Laboratory of the University of Leiden '''71''' pp. 3-25 (1901)</ref>
<ref>[http://www.digitallibrary.nl/proceedings/search/detail.cfm?pubid=436&view=image&startrow=1 H. Kammerlingh Onnes "Expression of the equation of state of gases and liquids by means of series", Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen '''4''' pp. 125-147 (1902)]</ref>. In the first case:
<ref>[http://www.digitallibrary.nl/proceedings/search/detail.cfm?pubid=436&view=image&startrow=1 H. Kammerlingh Onnes "Expression of the equation of state of gases and liquids by means of series", Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen '''4''' pp. 125-147 (1902)]</ref>, and mathematically by Ursell <ref>[http://dx.doi.org/10.1017/S0305004100011191 H. D. Ursell "The evaluation of Gibbs' phase-integral for imperfect gases", Mathematical Proceedings of the Cambridge Philosophical Society '''23''' pp. 685-697 (1927)]</ref>. One has
   
   
:<math> \frac{p V}{N k_B T } = Z = 1 + \sum_{k=2}^{\infty} B_k(T) \rho^{k-1}</math>.
:<math> \frac{p V}{N k_B T } = Z = 1 + \sum_{k=2}^{\infty} B_k(T) \rho^{k-1}</math>.

Revision as of 16:59, 20 November 2009

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 in 1885 by Thiesen [1] and extensively studied by Heike Kamerlingh Onnes [2] [3], and mathematically by Ursell [4]. One has

.

where

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

Virial coefficients

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

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

For a commentary on the convergence of the virial equation of state see [5] and section 3 of [6]

References

Related reading