Dieterici equation of state

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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 modification[edit]

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

References[edit]