- #1

Mbaboy

- 19

- 0

## Homework Statement

Derive the following:

[tex]

\mu_i=T\left( \frac{\partial S}{\partial n_i}\right)_{U,V,n_j\not=i}

[/tex]

[tex] \mu_i [/tex] is the chemical potential of the ith component

[tex] G [/tex] is the Gibbs free energy

## Homework Equations

[tex] dU = TdS - PdV + \sum_i \mu_i dn_i [/tex]

[tex] \mu_i = \left(\frac{\partial G}{\partial n_i}\right)_{p,T,n_j\not=i}[/tex]

## The Attempt at a Solution

I've tried to work it out but really haven't gotten anywhere. This is an engineering course, and up until now we haven't done anything like this or even used calculus. This is only a very small part of the question, but I figure if I can get this I'll be on the right track. I have little experience with multivariable calculus, so I guess that is my main problem. I'm sure there are other equations that could be used, but this was all that was given.

Thanks!

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