- #1
spaghetti3451
- 1,344
- 34
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?
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?