Song and Mason equation of state for hard convex bodies

The Song and Mason equation of state (EOS) for hard convex bodies is given by (Eq. 25 of Ref. 1):

${\frac {p}{\rho kT}}\approx 1+{\frac {\eta }{(1-\eta )^{3}}}\left((1+3\alpha )-(2+3\alpha -3\alpha ^{2})\eta +\left(1+\left[\left({\frac {B_{4}}{v_{0}^{3}}}\right)_{HS}-12\right]\alpha -7\alpha ^{2}\right)\eta ^{2}\right)$

where $\eta$ is the packing fraction, given by $\eta =\rho v_{0}$ where $v_{0}$ is the volume of one particle, and

$\alpha ={\frac {RS}{3v_{0}}}$

where $S$, the surface area, and $R$ the mean radius of curvature. $\left({\frac {B_{4}}{v_{0}^{3}}}\right)_{HS}$ is the fourth virial coefficient for the hard sphere model.

References

1. Yuhua Song and E. A. Mason "Equation of state for a fluid of hard convex bodies in any number of dimensions", Physical Review A 41 pp. 3121 - 3124 (1990)