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. The variables with subindex "c" refer to the critical values.

References

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