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):

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 \frac{p}{\rho k_B T} = \left[ 1- b_2 \eta - \frac{(1-b_2 \eta_{\mathrm{max}}) \eta^2}{\eta^2_{\mathrm{max}}} \right]^{-1}}

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 p} is the pressure, 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 \rho} is the number density, 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 k_B} is the Boltzmann constant, 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 T} is the temperature, 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 b_2=2} is the reduced second virial coefficient, 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 \eta = a_0(\sigma)\rho} is the packing fraction, with 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 a_0(\sigma) = (\pi/4)\sigma^2} the area of a hard disk with diameter 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 \sigma} , 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 \eta_{\mathrm{max}} = \pi \sqrt3 /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)