Virial Coefficients for a Hard-Sphere Mixture

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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.


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 ).


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



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


[1] Wikipedia. "Virial Coefficient." (Jun 3, 2014)

[2] Wikipedia. "Virial Expansion." (Jul 3, 2014)

[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.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.