Clausius equation of state

The Clausius equation of state is given by

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

where

$a=\frac{27R^2{T}_c^2}{64P_c}$

$b=v_c-\frac{R{T}_c}{4P_c}$

and

$c=\frac{3R{T}_c}{8P_c}-v_c$

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)