Solve Exact Differentials: Find G for dG = Vdp-Sdt

[Froskoy]

Homework Statement

Given that $$\mathrm{d}U = T\mathrm{d}S - p\mathrm{d}V$$

find a function $G$ such that $$\mathrm{d}G = V \mathrm{d} p - S \mathrm{d} t$$.

I'm not sure where to start - how are the two related? Could someone please give me a clue of how to start this off?

3. Attempt at the solution
I was thinking this looks too much like the quotient rule to be a coincidence...

With very many thanks,

Froskoy.

 

[lanedance]

$$dG = VdP - SdT$$

adding a few terms gives
$$dG = (VdP - SdT) + (VdP-VdP)+(TdS-TdS)$$

rearranging
$$dG = (VdP+PdV)-(SdT-TdS)- (PdV-TdS)$$

 

[pondhockey]

$$dG = VdP - SdT$$

adding a few terms gives
$$dG = (VdP - SdT) + (VdP-VdP)+(TdS-TdS)$$

rearranging
$$dG = (VdP+PdV)-(SdT-TdS)- (PdV-TdS)$$

So, what is the function G?

 

[Muphrid]

Do you know an expression for the function U in terms of T,S,P,V?

If so, think about what you could add or subtract to U in order to get the differentials to work for G.