Dieterici equation of state

The Dieterici equation of state is given by

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

where (Eq. 8 in ):

\[a = \frac{4R^2T_c^2}{P_ce^2}\]

and

\[b=\frac{RT_c}{P_ce^2}\]

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:

\[a = 2.99679 R T_c v_c\]

and

\[\eta_c = 0.357057\]