Clairaut's theorem: Difference between revisions

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{{Unreferenced|date=December 2009}}
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'''Critical variables''' are defined, for example in [[thermodynamics]], in terms of the values of variables at the [[critical point (physics)|critical point]].  
 
On a PV diagram, the critical point is an [[inflection point]]. Thus:
 
:<math>
\left(\frac{\partial P}{\partial V}\right)_{C}=0
</math>
:<math>
\left(\frac{\partial^2 P}{\partial V^2}\right)_{C}=0
</math>
 
For the [[van der Waals equation]], the above yields:  
 
:<math>
P_C=\frac{a}{27b^2}
</math>
:<math>
\displaystyle{V_C=3nb}
</math>
:<math>
T_C=\frac{8a}{27bR}
</math>
 
{{DEFAULTSORT:Critical Variable}}
[[Category:Thermodynamics]]
[[Category:Conformal field theory]]

Latest revision as of 09:49, 28 September 2014

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