Critical variable
From HandWiki
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:
- [math]\displaystyle{ \left(\frac{\partial P}{\partial V}\right)_{C}=0 }[/math]
- [math]\displaystyle{ \left(\frac{\partial^2 P}{\partial V^2}\right)_{C}=0 }[/math]
For the van der Waals equation, the above yields:
- [math]\displaystyle{ P_C=\frac{a}{27b^2} }[/math]
- [math]\displaystyle{ \displaystyle{V_C=3nb} }[/math]
- [math]\displaystyle{ T_C=\frac{8a}{27bR} }[/math]
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![]() | Original source: https://en.wikipedia.org/wiki/Critical variable.
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