Hint on problem 4 on PS2

In computing the entropy change of the environment, it is helpful to think of it as a constant T and P bath. We can write for the environment, at constant N,

dS = 1/T dE + P/T dV

Since the environment is a big bath, small changes of dE and dV do not affect its temperature or pressure. Therefore, we can integrate this equation to get:

DeltaS = (DeltaE + P * DeltaV) / T = DeltaH / T

Thus, if you know how much enthalpy the supercooled liquid gives up when it freezes, this must be the amount that is added to the environment, and so you can compute DeltaS for the environment this way.