Dieterici equation of state

The Dieterici equation of state is given by

$p={\frac {RT}{v-b}}e^{-a/RTv}$

where (Eq. 8 in ):

$a={\frac {4R^{2}T_{c}^{2}}{P_{c}e^{2}}}$

and

$b={\frac {RT_{c}}{P_{c}e^{2}}}$

where $p$ is the pressure, $T$ is the temperature and $R$ is the molar gas constant. $T_{c}$ is the critical temperature and $P_{c}$ is the pressure at the critical point.

Sadus modification

Sadus proposed replacing the repulsive section of the Dieterici equation with the Carnahan-Starling equation of state, which is often used to describe the equation of state of the hard sphere model, resulting in (Eq. 5):

$p={\frac {RT}{v}}{\frac {(1+\eta +\eta ^{2}-\eta ^{3})}{(1-\eta )^{3}}}e^{-a/RTv}$

where $\eta =b/4v$ is the packing fraction.

This equation gives:

$a=2.99679RT_{c}v_{c}$

and

$\eta _{c}=0.357057$