Santos-Lopez de Haro-Yuste hard disk equation of state

The Santos-Lopez de Haro-Yuste equation of state for hard disks (2-dimensional hard spheres) is given by (Eq. 2 Ref. 1, Eq. 5 Ref. 2, Eq. 1 Ref. 3):

${\frac {p}{\rho k_{B}T}}=\left[1-b_{2}\eta -{\frac {(1-b_{2}\eta _{\mathrm {max} })\eta ^{2}}{\eta _{\mathrm {max} }^{2}}}\right]^{-1}$

where $p$ is the pressure, $\rho$ is the number density, $k_{B}$ is the Boltzmann constant, $T$ is the temperature, $b_{2}=2$ is the reduced second virial coefficient, $\eta =a_{0}(\sigma )\rho$ is the packing fraction, with $a_{0}(\sigma )=(\pi /4)\sigma ^{2}$ the area of a hard disk with diameter $\sigma$, and $\eta _{\mathrm {max} }=\pi {\sqrt {3}}/6$

References

1. A. Santos, M. López de Haro, and S. Bravo Yuste "An accurate and simple equation of state for hard disks", Journal of Chemical Physics 103 4622 (1995)
2. Mariano López de Haro, Andrés Santos and Santos Bravo Yuste "A student-oriented derivation of a reliable equation of state for a hard-disc fluid", European Journal of Physics 19 pp. 281-286 (1998)
3. Mariano López de Haro, Andrés Santos, and Santos B. Yuste "Simple equation of state for hard disks on the hyperbolic plane", Journal of Chemical Physics 129 116101 (2008)