# Difference between revisions of "Dieterici equation of state"

The Dieterici equation of state [1] is given by

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

where (Eq. 8 in [2]):

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

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 [3] 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

$\eta_c = 0.357057$