WC1 and WC2 hard sphere equations of state

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

$Z_{WC1}=1+\sum _{n=2}^{10}B_{n}(\rho /\rho _{0})^{n-1}+(\rho /\rho _{0})^{10}\left[{\frac {B_{10}}{1-\rho /\rho _{0}}}-{\frac {0.68219}{(1-\rho /\rho _{0})^{2}}}\right]$

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

$Z_{WC2}=1+\sum _{n=2}^{m}B_{n}(\rho /\rho _{0})^{n-1}+(\rho /\rho _{0})^{m}\left[{\frac {B_{m}}{1-\rho /\rho _{0}}}-{\frac {A_{2}(\rho )}{(1-\rho /\rho _{0})^{2}}}\right]$

where (Eq. 8)

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 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 Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \rho } is the density where Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \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)