How do I solve this problem involving the Helmholtz and Gibbs Energy?

[Zach Sims]

1. Robert Dehoff 4.12
A system is designed that permits continuous programmed control of the pressure and volume of the gas that it contains. The system is filled with 1 g atom of helium and brought to an initial condition of one atmosphere and 18 liters. It is then reversibly compressed to 12 Liters along a programmed path given by the relationship.

V=2*P²+20

Where P is in atomospheres and V is in liters. Compute:
a Initial and Final temperatures
b Heat absorbed by the system
c The work done by the system
d The changes in U,H,F,G, and S

Homework Equations

There are many relevant equations to this problem. However, my main problem is the Gibb's and Helmholtz Energies. I have all the other values correct. The problem is I can't seem to find a way to express Gibb's and Helmholtz energy in a way that does not include an entropy term. I just don't know how to deal with them.

F = U-TS
G= H-TS

dH = 1520 J/mol
dU = 912 J/mol
T(initial)=215 K
T(Final)=292 K
dS = 0.26 J/(mol*k)

The Attempt at a Solution

I have been trying to write F as a function of T,P or V,P the problem is they always end up having some term of entropy. An example is my last attempt.

F(P,V) =-(S/P+P)dV+-S*(T/P)dP

And I just don't know how to solve these. I am just about to pull my hair out. I fee I am over complicating this and that the solution actually lies in a brief rearrangement of the relevant equation, but I cannot be sure.

Any help would be much appreciated.

 

[Chestermiller]

Well, you need to determine $\Delta (TS)$. But that is going to be a function of the value of S at some reference temperature. Are you allowed to use the ideal gas absolute entropy from statistical mechanics.? Or, are you allowed to use heats of formation, free energies of formation, and entropies of formation as being zero at 25 C and 1 atmosphere?

 

[Zach Sims]

Well, you need to determine $\Delta (TS)$. But that is going to be a function of the value of S at some reference temperature. Are you allowed to use the ideal gas absolute entropy from statistical mechanics.? Or, are you allowed to use heats of formation, free energies of formation, and entropies of formation as being zero at 25 C and 1 atmosphere?

I had a feeling that was the goal. I am not aware of any restrictions on the equations or paths we can take to a solution. I have tried to make an equation using the absolute entropy, but the equation seems at first confusing. Any guidance on how to first being my formulation would be much appreciated. Thanks.