Pure gas diagram P-V

These diagrams exist for many gases and can be digitized, replacing the curves with files P, V,T) which can be used in compnter calculations. 

These equations acconnt for a critical point whose coordinates are obtained by canceling ont the two primary partial derivatives of pressure with regard to volume. 

Under critical conditions (P Pc and T Tc), canceling out of the first derivative gives an eqnation that has either one or three roots. 

If such a state equation gives a single root, this proves that the system is monophasic and the root gives the molar volume of this phase. 

If such a state equation gives three roots, the lowest value of the molar volume obtained corresponds to the molar volume of the hquid and the highest value corresponds to the molar volume of the gas. The intermediate value has no physical sense and the P(T) curve between the two extreme roots is replaced by a horizontal line, since it represents a diphasic system in a hquid-vapor eqnihbrium and in this case the pressure is no longer a function of volume, it is constant while the two phases are present. 

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