 Hi, well, I'm Stephen Nashraba and I'm here to tell you a little bit about critical behavior of gases, and to do that, we'll start off with an indicator diagram, and if pressure on this axis, volume on that axis, and I've drawn some isotherms, so these are lines of constant temperature, and you're probably accustomed to, you know, isotherms that are even at a higher temperature here, which would follow Boyle's law, which would just be a simple hyperbolic function. But now we're getting at lower temperatures here, and as you can see, this what would have been a Boyle's isotherm has now developed a bit of a bump. Nevertheless, if you were following that gas, as you compressed it from high volume to low volume at a given temperature along an isotherm, what you would see is that the gas just gets compressed to a smaller and smaller volume, and nothing special happens, except that the gas just got denser and denser as you might expect. On the other hand, once it reaches below this certain critical point, which I've drawn here as this kind of step with an inflection point, let's go down to this even lower temperature, what would happen if you were compressing the gas that is going in this direction, compressing the gas, is that when you got to this very point right here, you would notice that a little bit of condensate formed at the bottom of your container, and as you compress it more and more, what happens is kind of interesting, the pressure doesn't go up anymore, it stays constant, but your active trying to compress the gas just produces, converts more of the gas into a liquid, until you get to this point when pretty much all the gas is now gone, you just have a little bit of liquid left, and so that all happens at this one pressure, and that pressure gets a special name, it's called P vape, okay, it's the vapor pressure at that particular temperature or for that isotherm, now of course once we've eliminated all the gas then now this is much steeper because if you try to compress a liquid now the pressure goes way up, you try to press down on it, so that leaves this middle isotherm, this is called the critical isotherm T critical, okay, and it's characterized by an inflection point right here, this is where the slope is zero, but also the second derivative is zero, that's the critical temperature, and as you can kind of see here that critical temperature, that inflection point also corresponds to a critical volume, and it also corresponds to a critical pressure, so it's a certain point and every gas has its own unique set of critical volumes, temperatures and pressure, okay, so all gases kind of do this, but the precise point at which this critical point occurs differs from gas to gas, so I've tabulated just two of them for you, carbon dioxide has a critical isotherm at 304 Kelvin, the critical volume occurs at 0.094 liters, okay, just a little bit less than a tenth of a liter, and that's on a per mole basis, and the critical pressure occurs at 73 atmospheres, if we're dealing with water, the actual physical circumstances are vastly different, we have to go to a much higher temperature, and the critical volume is a little bit smaller, and the critical pressure is also quite a lot higher, nevertheless the same qualitative features occur, we get this critical point below which condensation would occur along an isotherm, okay.