Critical variable

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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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