Show ##(\frac{\partial S}{\partial G})_Y = -\frac{C_Y}{TS}##

[GL_Black_Hole]

Homework Statement

Show that $(\frac{\partial S}{\partial G})_Y = -\frac{C_Y}{TS}$

Homework Equations

$G = H-TS, (\frac{\partial H}{\partial T})_Y = C_Y$

The Attempt at a Solution

$dG = dH -TdS -SdT$ and $H$ is a state variable so $dH =\frac{\partial H}{\partial T} dT + \frac{\partial H}{\partial Y} dY$. Not sure how to use the given information or continue from here.

 

[Charles Link]

What you have written makes little sense. I do think the $Y$ my actually be a $V$, but to take the partial derivative of $S$ w.r.t. $G$ is also rather odd.