Critical Variable

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:

$P_C=\frac{a}{27b^2}$

$\displaystyle{V_C=3nb}$

$T_C=\frac{8a}{27bR}$

Famous quotes containing the words critical and/or variable:

“Post-modernism has cut off the present from all futures. The daily media add to this by cutting off the past. Which means that critical opinion is often orphaned in the present.”
—John Berger (b. 1926)

“There is not so variable a thing in nature as a lady’s head-dress.”
—Joseph Addison (1672–1719)