Critical variable explained

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:^[1]

\left( (\partial P)/(\partial V) \right) _{C} =0 \left( (\partial ^{2} P)/(\partial V ^{2}) \right) _{C} =0

For the van der Waals equation, the above yields:

P _{C = (a)/(27 b ^{2})} \displaystyle{V _{C=3nb}} T _{C = (8 a)/(27 bR)}

Notes and References

1. Book: Sommerfeld, A. . Bopp . F. . Meixner . J. . Kestin . J. . Arnold Sommerfeld. 1956 . Thermodynamics and Statistical Mechanics - Lectures on Theoretical Physics Volume V . NY . Academic Press . 56-57.