Template:Short description 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:<ref name=Sommerfeld >Template:Cite book</ref>
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\left(\frac{\partial P}{\partial V}\right)_{C}=0 </math>
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\left(\frac{\partial^2 P}{\partial V^2}\right)_{C}=0 </math>
For the van der Waals equation, the above yields:<ref name=Sommerfeld/>
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P_C=\frac{a}{27b^2} </math>
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\displaystyle{V_C=3nb} </math>
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T_C=\frac{8a}{27bR} </math>