Critical variable

Critical variables are defined, for example in thermodynamics, in terms of the values of variables at the critical point.

On a PV diagram, the critical point is an inflection point. Thus:

: \left(\frac{\partial P}{\partial V}\right){C}=0 : \left(\frac{\partial^2 P}{\partial V^2}\right){C}=0

For the van der Waals equation, the above yields:

: P_C=\frac{a}{27b^2} : \displaystyle{V_C=3nb} : T_C=\frac{8a}{27bR}