Hey, everyone. So in earlier chapters in physics, we talked a lot about work, which is a transfer of mechanical energy. Remember, if you push a box, you're doing work on it, and it's going to gain some energy. In more recent videos, we've talked about heat, which is a transfer of another type of energy called thermal. And in this video, we're going to put these ideas together and we're going to talk about the first law of thermodynamics. What I'm going to show you is that it's just an equation and it relates heat and work with something called the internal energy of a system. This first law equation is going to be super important for the rest of thermodynamics, so it's really important that you get this down right. So let's check it out and we'll do a quick example together. So the equation for the first law is that ΔE=q-w. That's it. It's just 3 variables. What I want to mention though, however, is that you may also see this equation written as q+w. That's perfectly fine. That will also work. q-w has always made a little bit more sense to me, so that's the one we're going to use here at Clutch. But if you do see this q+w, I'm going to cover that in a later video. Alright. So this ΔE here refers to something called the change in internal energy of the system. And in most of your problems, the system will just be some kind of a gas, so these words are kind of interchangeable. This q here refers to a heat and it's the heat added to the system. So I'm going to write this as q₂. It also can be removed from the system, and I'll talk about that a little bit later as well. This w here refers to the work that gets done by the system, so I write this as w by. I'm always going to write it out like this because it's really important that you know the definitions for these terms and what they refer to. Alright. So let's just go ahead and see this equation in action in our first example here.

So in this example, we have to calculate the change in internal energy of gas. We're told that the work done by the gas is 200 joules, and we're going to add 500 joules of heat to the gas. So in this problem, we have internal energy, work, and heat. We're going to start off with the first law equation. So that's ΔE_internal of the system = heat added to the system - work done by the system. Right? It's just these three variables. If you want to calculate ΔE, then you just need the other two variables. You need q and w. It's as simple as that. So what is the heat added to the gas? Well, if you take a look at the problem here, we have two numbers, 500 and 200. Which one is it going to be? Well, hopefully, you guys realize we're adding 500 joules of heat to the gas. That's a dead giveaway that that's going to be this q. Continue with more details...