Editing Virial equation of state
Jump to navigation
Jump to search
The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 1: | Line 1: | ||
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 | density or the pressure. Such an expansion was first introduced by Heike Kamerlingh Onnes in 1901 <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> | <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: | ||
:<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>. | ||
Line 11: | Line 11: | ||
*<math> V </math> is the volume | *<math> V </math> is the volume | ||
*<math> N </math> is the number of molecules | *<math> N </math> is the number of molecules | ||
*<math> T </math> is the [[temperature]] | *<math>T</math> is the [[temperature]] | ||
*<math>k_B</math> is the [[Boltzmann constant]] | *<math>k_B</math> is the [[Boltzmann constant]] | ||
*<math> \rho \equiv \frac{N}{V} </math> is the (number) density | *<math> \rho \equiv \frac{N}{V} </math> is the (number) density | ||
Line 28: | Line 28: | ||
where ''f'' is the [[Mayer f-function]] (see also: [[Cluster integrals]]). | where ''f'' is the [[Mayer f-function]] (see also: [[Cluster integrals]]). | ||
See also | See also: | ||
*[http://dx.doi.org/10.1080/002689796173453 M. S. Wertheim "Fluids of hard convex molecules III. The third virial coefficient", Molecular Physics '''89''' pp. 1005-1017 (1996)] | |||
==Convergence== | ==Convergence== | ||
For a commentary on the convergence of the virial equation of state see <ref>[http://dx.doi.org/10.1063/1.1704186 J. L. Lebowitz and O. Penrose "Convergence of Virial Expansions", Journal of Mathematical Physics '''5''' pp. 841-847 (1964)]</ref> and section 3 of <ref>[http://dx.doi.org/10.1088/0953-8984/20/28/283102 A. J. Masters "Virial expansions", Journal of Physics: Condensed Matter '''20''' 283102 (2008)]</ref> | For a commentary on the convergence of the virial equation of state see <ref>[http://dx.doi.org/10.1063/1.1704186 J. L. Lebowitz and O. Penrose "Convergence of Virial Expansions", Journal of Mathematical Physics '''5''' pp. 841-847 (1964)]</ref> and section 3 of <ref>[http://dx.doi.org/10.1088/0953-8984/20/28/283102 A. J. Masters "Virial expansions", Journal of Physics: Condensed Matter '''20''' 283102 (2008)]</ref> | ||
==References== | ==References== | ||
<references/> | <references/> | ||
Line 39: | Line 38: | ||
*[http://dx.doi.org/10.1088/0034-4885/7/1/312 James A Beattie and Walter H Stockmayer "Equations of state", Reports on Progress in Physics '''7''' pp. 195-229 (1940)] | *[http://dx.doi.org/10.1088/0034-4885/7/1/312 James A Beattie and Walter H Stockmayer "Equations of state", Reports on Progress in Physics '''7''' pp. 195-229 (1940)] | ||
*Edward Allen Mason and Thomas Harley Spurling "The virial equation of state", Pergamon Press (1969) ISBN 0080132928 | *Edward Allen Mason and Thomas Harley Spurling "The virial equation of state", Pergamon Press (1969) ISBN 0080132928 | ||
[[category:equations of state]] | [[category:equations of state]] |