# Difference between revisions of "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 [1]. 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In terms of accuracy, the Thiele equation is superseded by the Carnahan-Starling equation of state