Helmholtz free energy of simple solid

[Kelsi_Jade]

The problem is :

a) Find Helmholtz free energy F(V, T) of a simple solid.
b) Use the result of part a) to verify that (∂F/∂T)_v and (∂F/∂V)_T are consistent with S(T, V) and P(V, T) in equation P=a₀T-b₀ln(V/V₀)

I know:
Helmholtz free energy is F=U-TS
and dF=-SdT-PdV
S=-((∂F/∂T)_v)
P=-(∂F/∂V)_T
Maxwell relation: (∂S/∂V)_T=(∂P/∂T)_V

My problem is that the only examples I have here of Helmholtz free energy is for an ideal gas, NOT a simple solid. Is this correct to say internal energy of simple solid is U=nc_vT+nu₀ ?
And S=nc_vln(T/T_r)+nRln(V/V_r+S(T_r, V_r) ?
Where you could just substitute the equations for U and S into F and simplify?

I found the above equations on a power point from another classes slides so I'm not sure on the background if they're accurate or not...

 

[member 553083]

Yes, those equations for the internal energy and entropy of a simple solid are correct. You can substitute them into the equation for Helmholtz free energy, F = U - TS, and simplify to obtain an expression for F(V, T). Then you can use the expression for F to verify that (∂F/∂T)v and (∂F/∂V)T are consistent with S(T, V) and P(V, T) in equation P=a0T-b0ln(V/V0).