Temperature of Phase Transition at Zero Pressure?

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SUMMARY

The discussion focuses on determining the temperature of phase transition, T0, at zero pressure for a solid with two phases characterized by specific energy equations: U1(S,V) = S²/a1 + b1V(V-2Vo) and U2(S,V) = S²/a2 + b2V(V-2Vo). The Clausius-Clapeyron relation is mentioned but deemed ineffective at zero pressure. The user attempts to equate the Gibbs free energy of both phases to find T0 but struggles with the cancellation of the TS term, indicating a need for further clarification on the approach to solving for T0.

PREREQUISITES
  • Understanding of Gibbs free energy and its role in phase transitions
  • Familiarity with the Clausius-Clapeyron relation
  • Knowledge of thermodynamic variables such as entropy (S) and volume (V)
  • Basic competency in calculus, particularly partial derivatives
NEXT STEPS
  • Review the Clausius-Clapeyron relation and its applications in phase transitions
  • Study the derivation and implications of Gibbs free energy equations
  • Explore methods for solving equations involving multiple variables and parameters
  • Investigate examples of phase transitions at zero pressure in thermodynamics
USEFUL FOR

Students and professionals in thermodynamics, particularly those studying phase transitions and Gibbs free energy, will benefit from this discussion.

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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