All of the phase changes we've been doing so far have been under constant pressure conditions, and, in particular, with the problems that I've been doing with water phase changes in the last couple of videos, it was at atmospheric pressure, at least at sea level atmospheric pressure, or at 1 atmosphere. So it was done-- well, I'll explain this diagram in a second. But we all know that in the universe, pressure isn't always constant and it definitely isn't always constant at 1 atmosphere. 1 atmosphere was defined as the pressure at sea level on Earth. Obviously, pressure will vary wildly if you go to smaller planets or larger planets, or have thicker atmospheres, or if we're just doing different types of applications dealing with gases and liquids and solids. So what I've drawn here is a phase diagram. Let me write that down. Phase diagram. And there are many forms of phase diagrams. This is the most common form that you might see in your chemistry class or on some standardized test, but what it captures is the different states of matter and when they transition according to temperature and pressure. This is the phase diagram for water. So just to understand what's going on here, is that on this axis, I have pressure. On the x-axis, I have temperature, and at any given point, this diagram will tell you whether you're dealing with a solid, so solid will be here, a liquid will be here, or a gas. For example, if I told you that I was at 0 degrees, let's say 0 degrees is right there, if I'm at 0 degrees Celsius and 1 atmosphere, where am I? So 0 degrees, 1 atmosphere, I'm right at that point right there. So I'm at a boundary point between solids and liquids at 1 atmosphere of pressure, right? This is when we're at 1 atmosphere of pressure. So this coincides with our traditional notion of when ice freezes or when it melts at 0 degrees. If we made the pressure higher, what happens? Well, then ice starts melting at a lower temperature, right? So this is pressure going up, so pressure going up, let's say-- I don't know what this is. This is maybe 10 atmospheres, ten times Earth's atmospheric pressure at sea level, then all of a sudden, the temperature at which solid turns into liquid -- this transition is solid to liquid -- the temperature at which that happens will go down. Likewise, if we lower the pressure, if we go to Denver and it's a mile high, pressure is lower because we have less of the atmosphere above us, then all of a sudden, the freezing point increases, so the freezing point will be something above 1 degree. This isn't drawn completely to scale, but the idea is your ice would actually freeze a little bit faster and would freeze at a higher temperature in Denver than it would at the bottom of the Dead Sea or in Death Valley at some below sea level point on the planet. Now, this transition is the transition between anything and gas. And we're very familiar, this is 1 atmosphere. And remember, this is water we're dealing with. This is the diagram for water, so at 1 atmosphere, this is kind of the stuff that we're used to seeing. Let me draw a line here. So at 1 atmosphere, 0 degrees is where solid, or ice, turns into liquid water. And then we go up here, so we keep going at a higher, higher, higher temperature, and then here, this would be, since we're at 1 atmosphere, this is 100 degrees Celsius right there. And that's the point at 1 atmosphere of pressure where liquid turns into gas, or water vaporizes, or the liquid boils. All of those are acceptable ways to think about that. But what happens when we go to low pressure? Once again, let's take our little trip to Denver. So that's Denver right there. It's not that drastic. I'm just doing that for education purposes. Or even better, let's say Mount Everest. Mount Everest, very low pressure there. Then our freezing point, we already said that goes up when you lower the pressure, and your boiling point goes down, so it's much easier to boil something on the top of Mount Everest than it is to boil it at the bottom or at the lowest point in Death Valley or the Dead Sea. The intuition behind that is if I have a liquid, a bunch of molecules in liquid form, and they're touching each other, but they have enough kinetic energy to move past each other, so they're flowing past each other, they're kind of rubbing up against each other, one of the reasons why they don't just evaporate, why this guy doesn't just jump up there, is that there's air above him. There's air pressure. And air pressure, we've learned about this when we did PV nRT. That's a bunch of gas molecules, and the pressure they're creating is essentially caused by their temperature and their kinetic energy. And they sit there, and they bounce, and they essentially keep these heavier molecules from going up. They keep them from essentially separating from each other and turning into a gas. So the more pressure you have, the harder it is for these guys to escape. On the other hand, if we're in a vacuum, if we're doing this on the surface of the moon and there's none of these guys there, then just a little slight bump, Even though this guy's still a little bit attracted to over here, they're still attracted to each other. But just a little bit of bump, since there's no pressure up here on the surface of the moon, might allow this guy to escape and go straight to a gas. So when you lower the pressure, it's just that much easier to go from liquid to gas or even from solid to gas. And you might say, Sal, that's a bizarre concept, solid to gas. It turns out, if you get to low enough pressures here, I mean, let's say this is-- Actually, there's probably none stuff here. This is probably close to a vacuum right here. You could go from ice-- So if you took ice and you were on the moon and you were at the right temperature-- this is maybe some negative degrees Celsius temperature I don't know what the exact temperature is -- your ice on the moon would go directly from ice to a gas. Because there's this huge vacuum here, so these molecules would say, hey, there's all this space to fill and if they just get bumped a little bit, they're just going to escape and turn into a gas. You might say, oh, Sal, that's a strange phenomenon. It only exists on the moon. And to rebut that comment, I've drawn the phase diagram for carbon dioxide. It's all around you. You're exhaling it as we speak. Your plants in the room are hopefully inhaling it but carbon dioxide at 1 atmosphere has a very different behavior than water. This is carbon dioxide at 1 atmosphere. Just so you know, this scale is definitely not drawn to scale. The difference between 1 atmosphere and 5 atmospheres is not the same as between 5 atmospheres and 73. Likewise, this is not drawn to scale here. This is a much larger distance than this. If I had to really draw it to scale, I'd have to stretch this chart out or do a logarithmic chart or something. But anyway, I was talking about carbon dioxide. So this is carbon dioxide solid, and this is gas, and this is liquid carbon dioxide. So at 1 atmosphere, let's say you live at sea level, like you're in New Orleans, I guess that's a little bit below sea level -- that's where I grew up -- if you were able to get your fridge down to minus 80 degrees Celsius, the carbon dioxide would actually freeze. And you're actually not too unfamiliar with that, or at least you haven't been if you've gone to some -- I don't know if they still use it for smoke machines or for visual effects on stage, but this is dry ice. It's frozen carbon dioxide. If you're at sea level atmospheric pressure, as soon as you get above this minus 78 and 1/2 degrees Celsius, it sublimates to gas. So that process, where you go straight from a solid to a gas, is sublimation. And that's why dry ice, when you see it, you don't see liquid dry ice or you don't see it at standard pressures. I've never seen liquid carbon dioxide. In fact, to get liquid carbon dioxide, you have to get above 5 atmospheres so you have to get above five times the sea level pressure on Earth, and you're really not going to see that in natural conditions on Earth. You might see that on Jupiter or Saturn where you have tremendous pressures because of the gravity and all of the atmosphere above you. Liquid carbon dioxide, you might see -- I don't know if Jupiter actually has carbon, but you'll probably see it on other huge massive planets that are gas giants. But on Earth, this process is just called sublimation. It's just a neat word. Or it's sublimating. It's going straight from solid to gas and it's something you've seen with dry ice. Now, there's a couple other interesting points here and you're probably already noticing them. This right here is called the triple point, because right here at this -- Well, in the case of carbon dioxide, at 5 atmospheres and minus 56 degrees Celsius, the carbon dioxide is in a state of equilibrium between the ice, the liquid and the gas. It's a little bit of all of the three. And if you just nudge it in one direction or another by nudging the pressure or the temperature, it'll go in that direction. Similarly, water's triple point is right here. It's at a much lower pressure than we're used to dealing with. This is 0.611 kilopascals, or just 611 pascals, which is 5/1000 of an atmosphere. So if you go down to 5/1000 of an atmosphere and you go a little bit above 0 degrees Celsius, you're at the triple point of water, where water can take on any of these states if you just nudge it in one direction or another. Now, the other interesting point on these charts is up here. This is the critical point. Sounds very important. Critical point. And that's the point at which if you increase the temperature beyond that or the pressure beyond that, you're dealing with a supercritical fluid. It sounds very exciting. So above here, you have a supercritical fluid. So very high temperature, very high pressure. It's so high temperature that it wants to be a gas, but you're putting so much pressure on it that it wants to be a fluid, so it's a little bit of both. And actually, in the case of water, supercritical water is actually used as a solvent. Because you can imagine, it's kind of like liquid water in that things can dissolve in it, but it's so high temperature and it can diffuse into solids that it's really good at just getting whatever you want out of whatever you're trying to clean or somehow get into or get salt put into the water. So this is supercritical fluid and it's a fun thing to think about. But anyway, I just wanted to expose you to these phase diagrams. Everything I've done so far was at a constant pressure and I changed the temperature, but you can also read them the other way. If I'm at 100 degrees, and I go from -- Well, let's say I'm at 110 degrees, where at sea level is comfortably in the gaseous phase for... So this is 110 degrees for water. It's water vapor. But if I were to increase the pressure and I keep increasing the pressure and maybe I dig a hole or something or I go into the ocean, then it's going to condense into water or it's going to condense into a liquid. If I did that experiment here, when I increase the pressure, I'm going to reverse sublimate. And I think I wrote down a word for what that is. Let me see if I wrote it down someplace. Oh, no, I didn't. I didn't write it down. But essentially it's something like condense, but the word is escaping me at the second. It's something on the word of condensing or falling together. Anyway, I forget the word, but it'll go straight from a gas to a solid. So these are pretty neat diagrams. They actually tell a lot about different substances and then tell you what happens when the pressure or the temperature changes.