Clausius equation of state

The Clausius equation of state is given by

$\left[p+{\frac {a}{T(v+c)^{2}}}\right](v-b)=RT$

where

$a={\frac {27R^{2}T_{c}^{2}}{64P_{c}}}$

$b=v_{c}-{\frac {RT_{c}}{4P_{c}}}$

and

$c={\frac {3RT_{c}}{8P_{c}}}-v_{c}$

where $p$ is the pressure, $T$ is the temperature, $v$ is the volume per mol, and $R$ is the molar gas constant. $T_{c}$ is the critical temperature and $P_{c}$ is the pressure at the critical point, and $v_{c}$ is the critical volume per mol.

References

1. R. Clausius "Über das Verhalten der Kohlensäure in Bezug auf Druck, Volumen und Temperatur", Annalen der Physik und Chemie 9 pp. 337-357 (1880)