 Hi, well, I'm Professor Nesheba, and I want to tell you a little bit about the differential form of the first law of thermodynamics. So key to this idea is that there's some exchange of energy between what we're going to call the system and the surroundings, and thermodynamics lays that out in two ways. Here I just kind of imagine that the surroundings are this hot plate and the system is the liquid in that beaker and you know, maybe the temperature of the hot plate of the surrounding is greater than the temperature of that water. In that case, we know that heat's going to go into that water. We measure the amount of heat that transfer that goes from system to surrounding or vice versa by this quantity Q, or if it's a tiny amount we're going to call it DQ, okay? A small amount of heat is positive if the temperature of the surroundings is bigger than the system. Likewise, if the temperature of the surroundings, if the surroundings are cooler than the system, then DQ will be negative when we imagine heat flowing out of the system into the surroundings. Okay, so that's one way that we talk about the exchange of energy between system and the surroundings. The other one is through work, and I've just imagined a tire pump here. Got a surrounding pressure. Got the some gas inside there, which is at a pressure. If the pressure of the surroundings right there is greater than the pressure in the air inside the tube, then we know that the, you know, assuming this can move, the volume will go down. And what we say is that DW is positive system that the surroundings do work on the system. Likewise, if we have less pressure in the surroundings, we can imagine that the at the system would expand, its volume would go up, and we have DW is negative. So that's all about the exchange of energy between the system and the surrounding. Now we get to the other half of this, which is that U is this quantity that we say is just a totality of all the energy in the system. And I'm going to say DU is the change in that energy resulting from some process. Okay? And now here's the first law of thermodynamics. It's pretty straightforward. It says that the change in the total energy of that system, DU, would have to be equal to whatever change that happened as a result of a temperature difference, plus whatever result that happens as a result of work, which in this case I've indicated is the change in volume. So that's the first law. And then one can think about a few limiting cases here. We've talked about temperature being greater than or less than the system and the surroundings. But what if they're equal? Or what if the temperatures are different, but there's an insulator between them? Either way, no heat is going to pass from a system to surroundings. So dq will be zero. What if the pressure is equal, and the system is equal to the pressure of the surroundings? We would say that the system is in mechanical equilibrium with the surroundings. Or maybe there's just some blockage that prevents the volume of the system from changing, no change in volume. Either way, we can't get any work done, and so we would call that dw equals zero. Okay.