WC1 and WC2 hard sphere equations of state

The WC1 and WC2 hard sphere equations of state are given by (Eq. 6):

$Z_{WC1}=1+\sum _{n=2}^{10}{B}_n(\rho /{\rho }_0{)}^{n-1}+(\rho /{\rho }_0{)}^{10}[\frac{B_{10}}{1-\rho /{\rho }_0}-\frac{0.68219}{(1-\rho /{\rho }_0{)}^2}]$

and WC2 (slightly more accurate) (Eq. 7)

$Z_{WC2}=1+\sum _{n=2}^m{B}_n(\rho /{\rho }_0{)}^{n-1}+(\rho /{\rho }_0{)}^m[\frac{B_m}{1-\rho /{\rho }_0}-\frac{A_2(\rho )}{(1-\rho /{\rho }_0{)}^2}]$

where (Eq. 8)

$A_2(\rho )=\frac{\exp (B_{m+1}-B_m)-(\rho /{\rho }_0)(B_m-B_{m-1})}{\rho /{\rho }_0-\exp (1)}$

where $B$ are the hard sphere virial coefficients and $\rho$ is the density where ${\rho }_0=\sqrt{2}/{\sigma }^3$ and $\sigma$ is the hard sphere diameter.

References

Related reading

• Leslie V. Woodcock "Virial Equation-of-State for Hard Spheres", arXiv:0801.4846v3 2 Feb (2008)