Virial Coefficients for a Hard-Sphere Mixture

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The equation of state of an imperfect gas can be represented as an expansion of the pressure in powers of the density , where is the Boltzmann constant, is the absolute temperature, and is the virial coefficient. In the case of a binary mixture of hard spheres, the virial coefficients are functions of the diameters ( and ) of the two components and of the mole fraction of the larger-sphere component. The coefficients , , and all the contributions to (except one) are known exactly, and an excellent empirical approximattion for the additional contribution to is available.

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The Demonstration plots the second, third, and fourth virial coefficients (), scaled with , as functions of either the mole fraction (for variable size ratio ) or the size ratio (for variable mole fraction ).

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Contributed by: Andrés Santos (July 2014)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The analytical expressions for the fourth virial coefficients can be found in [3] and [4].

References

[1] Wikipedia. "Virial Coefficient." (Jun 3, 2014) en.wikipedia.org/wiki/Virial_expansion.

[2] Wikipedia. "Virial Expansion." (Jul 3, 2014) en.wikipedia.org/wiki/Virial_coefficient.

[3] S. Labík and J. Kolafa, "Analytical Expressions for the Fourth Virial Coefficient of a Hard-Sphere Mixture," Physical Review E, 80, 2009 051122. doi:10.1103/PhysRevE.80.051122.

[4] I. Urrutia, "Analytical Behavior of the Fourth and Fifth Virial Coefficients of a Hard-Sphere Mixture," Physical Review E, 84, 2011 062101. doi:10.1103/PhysRevE.84.062101.



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