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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(rac{partial P}{partial V}
ight)_{C}=0

:$$
left(rac{partial^2 P}{partial V^2}
ight)_{C}=0

For the van der Waals equation, the above yields:
:$$
P_C=rac{a}{27b^2}

:$$
displaystyle{V_C=3Nb}

:$$
T_C=rac{8a}{27bR}