Nezbeda equation of state for hard convex bodies

The Nezbeda equation of state (EOS) for hard convex bodies is given by (Eq. 13 in Ref. 1)

$Z={\frac {P}{\rho kT}}={\frac {1+(3\alpha -2)y+(\alpha ^{2}+\alpha -1)y^{2}-\alpha (5\alpha -4)y^{3}}{(1-y)^{3}}}$

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 y} is the packing ratio, given by 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 y=\rho V} , 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 \alpha= \frac{RS}{3V}}

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 V} is the volume, $S$, the surface area, 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 R} the mean radius of curvature.

References

1. I. Nezbeda "Virial expansion and an improved equation of state for the hard convex molecule system", Chemical Physics Letters 41 pp. 55-58 (1976)