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:

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

where

• $p$ is the pressure

• $V$ is the volume

• $N$ is the number of molecules

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

• $B_{k}\left(T\right)$ is called the k-th virial coefficient

Systems

• Hard spheres
• Hard disks