 Hi, I'm Professor Nashaba and I want to tell you a little bit about enthalpy versus internal energy. So the internal energy, as we know, that's just adding up all the internal kinetic and potential energy that a system has. And by contrast, the enthalpy says take that number, we just calculated it, and add to it that product which is, this is my system. It has a certain pressure and a certain volume. We multiply those two together and add that to the internal energy and we get the enthalpy. So one thing that you can see right off the bat is that the enthalpy is generally bigger than the internal energy because we're adding a little bit to it. How about in terms of the differential equation of state? Well, here we have a picture of u as a function of temperature and volume. So it's the internal energy in a temperature volume state space and the slope in the temperature direction we call Cv, the constant volume heat capacity. The slope in the volume direction is called pi sub t. So that's what these surfaces look like and it's kind of described by that differential equation of state there. A few things. Pi sub t is zero for an ideal gas and generally not zero for a real gas. And Cv sort of tells us when we're heating up a substance isochorically, so along that sort of line that is at a constant volume, we know that Cv is the proportionality constant between how much the temperature goes up and how much heat went into the system. How does that work for this scenario? Well, we like to think about the enthalpy in a temperature and pressure state space and it looks kind of similar. The slope in the temperature direction is called Cp, the constant pressure heat capacity. The slope in the pressure direction is a new quantity called mu sub t. That's the isothermal joule-tompson coefficient. Similarly, for an ideal gas, mu sub t is zero and that surface is flat in the pressure direction. We also write a differential equation of state pretty similarly. Changes in the enthalpy are given by changes in the temperature times Cp. That slope plus changes in the pressure times the isothermal joule-tompson coefficient. And what about that Cp? Well, we just define the heat capacity to be this way. If I'm going to be heating up my substance while holding the pressure constant, that would be isobaric heating. If the temperature goes up by a certain amount, then I multiply that by this constant or that number Cp and that tells me how much heat goes in or out. Last thing, going back to the internal energy in a volume temperature state space, the first law says something like this. The change in the internal energy in general is equal to the work done plus the heat that goes in or out. But if we have isobaric heating, then I can put a little subscript v there and I say that term goes away. So the nice thing about this is that the change in the temperature, which gives me the heat that goes in and out, tells me directly about how much the internal energy changed. How does that work in enthalpy land? Well, it goes something like this. We haven't proved this, but I can tell you that it's possible to show that under certain circumstances a very similar thing works. Namely, once I figured out how much heat goes in to the system by multiplying the temperature change by Cp, I can tell you that that heat that goes in is exactly equal to the amount that the enthalpy went up, which it does follow from the first law, but it takes a few assumptions that goes into showing that that is true. Okay.