WC1 and WC2 hard sphere equations of state

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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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)

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 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 (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B} are the hard sphere virial coefficients and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho} is the density where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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)