Temperature of Phase Transition at Zero Pressure?

[S_Flaherty]

Homework Statement

There is a solid that can be in two phases, with energies U₁(S,V) = S²/a₁ + b₁V(V-2V_o) and U₂(S,V) = S²/a₂ + b₂V(V-2V_o).

Consider a phase transition between the two phases at zero pressure.

At what temperature, T₀, does it occur?

Homework Equations

T = ∂G/∂S
dP/dT = L/TΔV

The Attempt at a Solution

I'm not sure about all the equations that would be relevant. I was thinking that I would need to use the Clausius-Clapeyron relation but if P = 0 then that gets me nowhere. Then I thought about setting the Gibbs free energy at each phase equal to each other which would give me
S²/a₁ + b₁V(V-2V_o) - TS = U₂(S,V) = S²/a₂ + b₂V(V-2V_o) - TS but the TS on each side would cancel out and I wasn't sure what I would have to do in order to get T₀.

Am I going in the completely wrong direction in trying to figure this out?

 

[S_Flaherty]

Anyone?

 

[S_Flaherty]

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