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

$b=\frac{R{T}_c}{P_c{e}^2}$

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, 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:

$a=2.99679R{T}_c{v}_c$

and

${\eta }_c=0.357057$