Thiele hard sphere equation of state

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.