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. (Eqn. 10 in Ref 1).

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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:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \eta = \frac{ \pi }{6} \frac{ N \sigma^3 }{V} }

• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma } is the Hard Sphere diameter.

References

1. N. F.Carnahan and K. E.Starling,"Equation of State for Nonattracting Rigid Spheres" J. Chem. Phys. 51 , 635-636 (1969)