I'm curious how do you choose the u and v transformations here to be equal to the constants and why is the f(u,v)=1 for the area- because you are summing infinitesimal x's and y's? I see that the area in xy is difficult to integrate because the sides are curved. is the transformation proven somewhere?(adsbygoogle = window.adsbygoogle || []).push({});

problem statement: the work done by an ideal Carnot engine is equal to the area enclosed by two isotherms and adiabatic curves. [tex]xy=a, xy=b, xy^{1.4}=c, xy^{1.4}=d[/tex][tex]\begin{bmatrix}\frac{\partial x}{\partial u}\ & \frac{\partial x}{\partial v}\\ \frac{\partial y}{\partial u} &\frac{\partial y}{\partial v}\\ \end{bmatrix}=\frac{5}{2v}, \int_{c}^{d}\int_{a}^{b}\frac{5}{2v}dudv=\frac{5}{2}(b-a)ln\frac{d}{c}[/tex]

by the way, how long does it take people to do these?

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# Work of Carnot Engine integral

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