Parsons equation of state for hard rods

The Parsons equation of state (EOS) for hard rods is given by (Eq. 22 of Ref. 1)

${\frac {pV}{NkT}}-1=4\eta \alpha (\eta )$

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 \eta} is the packing fraction, 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 \alpha(\eta)} was substituted for the Carnahan-Starling equation of state.

References

1. J. D. Parsons "Nematic ordering in a system of rods", Physical Review A 19 pp. 1225 - 1230 (1979)