Parsons equation of state for hard rods

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

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\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)