/sci/ - Science & Math

Our professor defined [math]T=h\nu-\phi[/math], where [math]\phi[/math] is the work function (also defined as the energy needed to remove an electron of a solid surface). But in wikipedia the work function is defined as [math] W=-e\phi-E_f[/math], or [math]\phi=V-\frac W e[/math], where W is the work function meanwhile [math]\phi[/math],es the electrostatic potential. Are both definitions equivalent and I just can't see it or are they defining different things?

A substance has the following properties:
>at T = T0 = cte, the work done by a reversible expansion from V0 to V is [math]W = RT_0 ln(\frac{V }{V_0})[/math]
>the entropy is given by [math]S=R(\frac{V_0}{V})(\frac{T}{T_0})^a[/math], (V0, T0 and a constants.).
Calculate the Helmoltz free energy.

So the Helmoltz free energy is F=E-TS and dF=-SdT-pdV, so at T constant [math]dF=RT_0 ln(\frac{V }{V_0})[/math]. But how do I get F from here?