Temperature of Phase Transition at Zero Pressure?

S_Flaherty
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Homework Statement


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

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-2Vo) - TS = U2(S,V) = S2/a2 + b2V(V-2Vo) - 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?
 
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