Is the latent heat associated with phase transitions correlated with the temperature at which they occur?
The latent heat is related to the difference in energy between the two phases, and the temperature of the phase transition occurs at the point where the difference in energy between the two phases is comparable to thermal fluctuations. What factors would lead to departures from a linear relationship between the two, e.g. in different materials or different phase transitions in the same material? Or is there an error in my assumptions?
Best Answer
Let me state first that one should not speak about energies but about free energies, as soon as temperature is not absolute zero. Discussion of energies has in this case no sense.
Second, a very simple answer to the original question is pointing out that according to its definition the heat, $Q = T \Delta S$, where $S$ is entropy, $\Delta S$ is its difference in the two states. You may find discussion of this point in the 5th volume of Landau and Lifshitz's book, Eq. (13.4) and around. This is valid also for the latent heat. Thus, the answer, is yes, it depends upon temperature. This alone does not give one too much, since one needs to know the entropies in the both phases.
Third, you are wrong to think that transition takes place "at the point where the difference in energy between the two phases is comparable to thermal fluctuations". That is simply an error. The condition of any phase transition is $F_1=F_2$, where $F_{1,2}$ are the phases free energies. One may use also other thermodynamic potentials instead depending upon details of the problem statement. In the case of the 2nd order transition one can use a more simple relation, but the equality $F_1=F_2$, nevertheless, stays behind that relation.
Your question "What factors would lead to departures from a linear relationship between the two, e.g. in different materials or different phase transitions in the same material?" is completely unclear to me, but in any case I would not strongly expect anything related to phase transitions to be linear.