Oil and water -- they don't mix. Or do they? Due to the entropy of mixing, any tiny amount of impurity is highly favored entropically. This means that in general, you can get a small amount of a substance to mix into another. But take that too far, and they no longer mix, but "phase separate" into 2 different concentrations. We discuss this from the following perspectives: energy, entropy, and free energy. Examples: binary alloy with interactions, and a mixture of He3 (fermions) and He4 (bosons).
Class discussion: Can you get oil and water to mix if you heat them in a pressure cooker? Lecture Audio