 So, what we understand about phase transition so far, in particular, how the free energy changes, the Gibbs free energy changes with temperature tells us that as we heat a substance, solid will eventually become less stable than the liquid. Liquid will eventually become less stable than the gas. Free energies are decreasing for each of these substances, but at a faster rate for the one that have higher entropy like the gas, and at a slower rate for the ones that have low entropy like the solid. On this version of the diagram, I've included as dotted lines the phases that are not the most stable phase. So at cold temperatures where the solid's most stable, the solid has the stable line. Once we pass the melting point where the liquid is the most stable phase, that's the one with the solid line. At high temperatures above the boiling point, the gas has the solid line. There are still curves. I can still calculate what the free energy of the liquid would be at temperatures below the melting point, but since it's not the most stable phase, since it's got a higher free energy than the solid does, we typically don't observe the liquid at those cold temperatures below the melting point. If we are at equilibrium, if I have a liquid, if I have water at room temperature in this room, for example, under conditions like this, the phase that we would observe would be the liquid phase, the one with the lowest free energy. If I start lowering the temperature in this room from room temperature down towards and then across the freezing point, what's going to happen is when I get to the freezing point, the water will convert to solid. The water will freeze. So that's what happens if I'm in equilibrium, if I do that process slowly enough to remain in equilibrium. But there are conditions where I can get away from equilibrium. If I take the liquid and I cool it too quickly, I can remain on the liquid curve without remaining in equilibrium, without converting to the solid. There's other ways of remaining in the non-equilibrium state as well. I could either cool the liquid very rapidly or sometimes, and you may have seen videos of this. There's relatively common YouTube videos. I'll post a link to some where you can cool a liquid that's pure enough not to have any impurities that serve as nucleation sites for the liquid to nucleate and become ice crystals. It's actually relatively easy to cool to temperatures several degrees below the freezing point and yet remain in the liquid phase. And then it just takes a slight perturbation to cause the liquid to crystallize and form ice. So we rapidly fall down from this non-equilibrium liquid curve down to the equilibrium solid curve. That process where we don't obey what equilibrium and Boltzmann says we should do, but instead we remain in the less stable liquid phase to temperatures below the freezing point before converting down to the solid phase. That's called supercooling. We can supercool water not just to the freezing point, but below the freezing point. That's if we remain out of equilibrium in a non-equilibrium process. The same thing is true for other phase transitions like the boiling point. If we pass the boiling point under equilibrium conditions, then of course the liquid will reach the boiling point and then we'll have a reversible equilibrium transition from liquid converting to gas and we'll boil the gas. On the other hand, if we do it under non-equilibrium conditions, it's possible to superheat. In fact again it's relatively easy to superheat the liquid and get it above the normal boiling point by several degrees without having converted to a gas. You can see here if I just get a few degrees above the boiling point there's a large difference in energy, a Gibbs free energy anyway, between the liquid, the superheated non-equilibrium liquid state, and the more stable gas state. What will happen if the system is allowed to recover back to equilibrium, it will very quickly and irreversibly convert to the gas phase and give off quite a bit of energy when it does that. If you've been in a chemistry lab, most likely you've experienced this phenomenon or you've used boiling chips when you boil a liquid to avoid experiencing this phenomenon. The reason we use boiling chips in a flask of solvent is to avoid superheating the solvent and causing that rapid boiling of the solvent, which gives off a lot of energy and causes bumping in the fluid. If you've ever experienced bumping in your flask of solvent, that's the thing we use the boiling chips to avoid. It's the superheated liquid rapidly converting to a gas rather than in a reversible equilibrium manner converting to a gas. Any phase transition we can perform it in an equilibrium way or a non-equilibrium way. Very often in the course we're going to assume that we're doing things under equilibrium conditions but in the real world that's not always the case. This is just a brief reminder that the diagrams we draw for the equilibrium case and the next thing we'll do is revisit what these phase transitions look like not just as we examine the free energy as a function of temperature but when we examine free energy as a function of another variable the pressure.