Calculate Helmholtz Free Energy with Entropy, Work given [closed]

it's my first time here and I hope the post complies with the general rules.

My problem originates here: I'm doing a statistical physics task which unfortunately leaves me clueless atm. I keep my question general at first since I believe I will be able to do the calculus on my own and I simply lack some presence of mind for this:

Given is some gas with a relation for entropy: $S(T,V,N)$ and a relation for isothermal work when expanding/contracting the volume from $V_0$ to $V$. I also presume that we say $N = const.$, since we've not yet introduced variation in particle numbers.

So I've tried to use the differential $dF = -SdT-pdV$, because I assumed I could use the integrability condition $(\frac{dS}{dV})_T = (\frac{dp}{dT})_V$. I also tried to use, that for an isothermal process should hold $dF = dW$. However, all these doesn't seem to work out decently. I feel stupid. Any good ideas?

Edit: Thanks for preventing others from giving an 'official' hint, nevermind.

I've figured it out. After all, the approach is indeed to use that for an isothermal process $dF = dW$ is true, with which you can find out the pressure for the given Temperature, $-p(T_0)$. Then you have both quantities for the total differential and can integrate it, which yields the general expression of $F$ for arbitrary temperatures, $F(T,V)$. With $-p = (\frac{dF}{dV})_T$ one can gain the equation of state for p and calculate the remains.

closed as off-topic by Danu, ACuriousMind♦, Rob Jeffries, Kyle Kanos, NeuneckNov 28 '14 at 6:34

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – Danu, ACuriousMind, Rob Jeffries, Kyle Kanos, Neuneck
If this question can be reworded to fit the rules in the help center, please edit the question.

• sorry I am not sure exctly what you question it is you are asking - can you make clearer the information you have been given and what you want to derive? (p.s. You are very welcome here) – tom Nov 27 '14 at 19:56
• Thank you for the welcome. I've added the whole task, hope it's more clear now. – failtrolol Nov 27 '14 at 20:15
• I've figured out how to solve it. It remains quite unclear for me what was wrongly done, whatsoever. – failtrolol Nov 30 '14 at 12:46