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}}

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