Virial Coefficients for a Hard-Sphere Mixture

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 ).


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+