Virial coefficients of model systems

The virial equation of state is used to describe the behavior of diluted gases. It is usually written as an expansion of the compresiblity factor, $Z$, in terms of either the density or the pressure. In the first case:

$\frac{pV}{N{k}_{B}T}=Z=1+\sum _{k=2}^{\mathrm{\infty }}{B}_k(T){\rho }^{k-1}.$

where

• $p$ is the pressure

• $V$ is the volume

• $N$ is the number of molecules

• $\rho \equiv \frac{N}{V}$ is the (number) density

• $B_k$ is called the k-th virial coefficient

Systems

• Hard spheres
• Hard disks