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)

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 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 $y$ 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, 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 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)