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The Thiele hard sphere equation of state is an equation of state for a hard sphere fluid developed by Thiele in 1963 . The equation provides a better approximation of the repulsive forces between molecules than the Van der Waals repulsive term. The equation is given below: $Z_{hs} = \frac{p_{hs}V_m}{RT} = \frac{1 - \eta^3}{(1-\eta)^4} = \frac{1 + \eta + \eta^2}{(1-\eta)^3}$,

where: $Z_{hs}$ is the compressibility factor of the hard sphere fluid; $p_{hs}$ is the pressure of the fluid; $V_m$ is the molar volume of the fluid; $T$ is the absolute temperature of the fluid; $R$ is the gas constant; and $\eta$ is the packing fraction of the fluid.

In terms of accuracy, the Thiele equation is superseded by the Carnahan-Starling equation of state