Carnahan-Starling equation of state

The equation of Carnahan-Starling is an approximate equation of state for the fluid phase of the Hard Sphere model in three dimensions.

$Z={\frac {pV}{Nk_{B}T}}={\frac {1+\eta +\eta ^{2}-\eta ^{3}}{(1-\eta )^{3}}}.$

where:

• $p$ is the pressure

• $V$ is the volume

• $N$ is the number of particles

• $k_{B}$ is the Boltzmann constant

• $T$ is the absolute temperature

• $\eta$, is the packing fraction:

$\eta ={\frac {\pi }{6}}{\frac {N\sigma ^{3}}{V}}$

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