Critical variable

{{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.

On a PV diagram, the critical point is an inflection point. Thus:{{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}}

:$$

\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}