# 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)