Editing Critical variable (section)

{{Short description|Thermodynamic variables associated with critical points}}
'''Critical variables''' are defined, for example in [[thermodynamics]], in terms of the values of variables at the [[critical point (physics)|critical point]]. 

On a PV diagram, the critical point is an [[inflection point]]. Thus:<ref name=Sommerfeld >{{cite book | last = Sommerfeld | first = A. | editor-last1 = Bopp | editor-first1 = F. | editor-last2 = Meixner | editor-first2 = J. | translator-last = Kestin | translator-first = J. |author-link=Arnold Sommerfeld| date = 1956 | title = Thermodynamics and Statistical Mechanics - Lectures on Theoretical Physics Volume V | location = NY | publisher = Academic Press | pages=56-57}}</ref> 

:<math>
\left(\frac{\partial P}{\partial V}\right)_{C}=0
</math>
:<math>
\left(\frac{\partial^2 P}{\partial V^2}\right)_{C}=0
</math>

For the [[van der Waals equation]], the above yields:<ref name=Sommerfeld/>

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