Alder-Hoover-Young hard disk equation of state

The Alder-Hoover-Young hard disk equation of state is given by (Ref. 1 Eq. 1)

$Z={\frac {pV}{Nk_{B}T}}={\frac {D}{\alpha }}+C_{0}+C_{1}\alpha$

where Z is the compressibility factor, $C_{0}=1.90\pm 0.01$ and $C_{1}=0.67\pm 0.07$ 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 D} is the dimensionality of the system, i.e. for hard disk 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 D=2} .

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{V-V_0}{V_0}}

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_0} is the close packed volume.

References

1. B. J. Alder, W. G. Hoover, and D. A. Young "Studies in Molecular Dynamics. V. High-Density Equation of State and Entropy for Hard Disks and Spheres", Journal of Chemical Physics 49 pp. 3688-3696 (1968)