Fundamental equation and state equations of the ideal gas

[fluidistic]

Homework Statement

Find the fundamental equation of a monoatomic ideal gas in the Helmholtz potential representation, in the enthalpy representation, and in the Gibbs function representation. Assume the fundamental equation $S= \frac{NS_0}{N_0} +NR \ln \left [ \left ( \frac {U}{U_0} \right ) ^{3/2} \left ( \frac{V}{V_0} \right ) \left ( \frac {N}{N_0} \right ) ^{-5/2} \right ]$. In each case find the equations of state by differentiation of the fundamental equation.

Homework Equations

Helmholtz: F=U-TS. But F(T,V,N)
PV=NRT.
$U=\frac{3NRT}{2}$.

The Attempt at a Solution

I first deal with Helmholtz.
If I understand well, I must get F(T,V,N)=U-TS. I already have U in terms of T and N. The last task is therefore to get S in terms of T,V and N which seems easily made by using the given fundamental equation.
It gives me $F(T,V,N)=\frac {3NRT}{2}-T \{ NK_1 +NR \ln \left [ \left ( \frac{V}{V_0} \right ) \left ( NTK_2 \right ) ^{3/2} \left ( \frac{N}{N_0} \right ) ^{-5/2} \right ] \}$.
So far I wonder if my approach is a right one. Is it ok so far?

 

[I like Serena]

I just got a reminder that this question went unanswered.
Tbh, I have no clue. Well... maybe if I think hard about it...
Erm... @fluidistic, can you perhaps write an answer by now?