Lesson plan

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}

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Article summary

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}

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