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

$b={\frac {RT_{c}}{P_{c}e^{2}}}$

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 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:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a = 2.99679 R T_c v_c}

and

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \eta_c = 0.357057}