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:

“Probably more than youngsters at any age, early adolescents expect the adults they care about to demonstrate the virtues they want demonstrated. They also tend to expect adults they admire to be absolutely perfect. When adults disappoint them, they can be critical and intolerant.”
—The Lions Clubs International and the Quest Nation. The Surprising Years, I, ch.4 (1985)

“Walked forth to ease my pain
Along the shore of silver streaming Thames,
Whose rutty bank, the which his river hems,
Was painted all with variable flowers,”
—Edmund Spenser (1552?–1599)