- #1
astropi
- 47
- 0
So, this is not a homework problem. Merely for my own understanding.
This is (or should be) relatively simple I believe. Anyway, start of with Gibbs free energy and take the derivate, we arrive at:
[tex] dG = -SdT + VdP + \mu dN[/tex]
take the partials we can see that with respect to dP we get V, with respect to dT we get -S, and with respect to dN we get mu. So far so good. Now, I know that if you take
[tex] \partial\mu / \partial P = V/N [/tex]
but I'm just not seeing it? Is this not simply taking the derivative of G once more with respect to N? I think I'm missing something simple, so any help is appreciated. Thanks.
This is (or should be) relatively simple I believe. Anyway, start of with Gibbs free energy and take the derivate, we arrive at:
[tex] dG = -SdT + VdP + \mu dN[/tex]
take the partials we can see that with respect to dP we get V, with respect to dT we get -S, and with respect to dN we get mu. So far so good. Now, I know that if you take
[tex] \partial\mu / \partial P = V/N [/tex]
but I'm just not seeing it? Is this not simply taking the derivative of G once more with respect to N? I think I'm missing something simple, so any help is appreciated. Thanks.