# Thiele hard sphere equation of state

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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
^{[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:

,

where:

- is the compressibility factor of the hard sphere fluid;
- is the pressure of the fluid;
- is the molar volume of the fluid;
- is the absolute temperature of the fluid;
- is the gas constant; and
- is the packing fraction of the fluid.

In terms of accuracy, the Thiele equation is superseded by the Carnahan-Starling equation of state