Dieterici equation of state: Difference between revisions

Revision as of 15:05, 22 September 2010

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^{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 ^[3] 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=2.99679RT_{c}v_{c}

and

\eta _{c}=0.357057

@@ Line 16: / Line 16: @@
 Sadus <ref>[http://dx.doi.org/10.1063/1.1380711 Richard J. Sadus "Equations of state for fluids: The Dieterici approach revisited", Journal of Chemical Physics '''115''' pp. 1460-1462 (2001)]</ref> proposed replacing the repulsive section of the Dieterici equation with the [[Carnahan-Starling equation of state]], resulting in (Eq. 5):
-:<math>p = \frac{RT}{v} \frac{ 1 + \eta + \eta^2 - \eta^3 }{(1-\eta)^3 }  e^{-a/RTv}</math>
+:<math>p = \frac{RT}{v} \frac{(1 + \eta + \eta^2 - \eta^3)}{(1-\eta)^3 }  e^{-a/RTv}</math>
 where <math> \eta = b/4v </math> is the [[packing fraction]].
+This equation gives:
+:<math>a = 2.99679 R T_c  v_c</math>
+and
+:<math>\eta_c = 0.357057</math>
 ==References==