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# Proving the Joule-Thomson Effect

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I wonder how one can use a partial derivative with constrain slope dH= 0 in a general equation with two partial derivatives where dH=0 is not true. The problem is for the Joule-Thomson effect. The question is much better described in the attachment. This is a problem from chemistry but since it is just mathematical I thought I might as well ask it in the math help part.

https://brainmass.com/math/calculus-and-analysis/proving-joule-thomson-effect-555845

#### Solution Preview

The reason why dH= 0 is because in the Joule-Thomson effect experiment, H is a constant (the derivative of constant is zero). I will show you why H is a constant.

Suppose the gas occupies a volume V1 at a pressure P1 ...

#### Solution Summary

The solution gives detailed discussion on partial derivative on the applicaiton of chemstry: Joule-Thomson Effect.

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