Gibbs free energy partial derivative

[spaghetti3451]

g = u + Pv - Ts

To find the partial derivative of g with respect to T at constant P, we do the following.

dg = du + vdP + Pdv - Tds - sdT and du = Tds - Pdv.

Therefore, dg = vdP - sdT.

At constant pressure, dg = - sdT.
Therefore, the partial derivative is - s.

I think we could have found this result equally well by just taking the derivative of g with respect to T keeping P constant. u, v and s are constant, so the answer is - s.

Which method do you think is the right one?

 

[Bill_K]

The method you've detailed above is the right one. It's not true where you say that u, v and s are constant -- they're not.

 

[spaghetti3451]

Just to confirm: Are you saying that the first method is correct and the second is not?

Why are u, v and s not constant?