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

).