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:

“Most critical writing is drivel and half of it is dishonest.... It is a short cut to oblivion, anyway. Thinking in terms of ideas destroys the power to think in terms of emotions and sensations.”
—Raymond Chandler (1888–1959)

“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)