Hey, guys. So throughout our discussion on thermodynamics, we'll often be talking about gases. And specifically, we'll be talking about these things called ideal gases. So in this video, I want to introduce to you what an ideal gas is and the equation that we use for them, which is called the ideal gas law. So let's get started here. What is an ideal gas? Well, the definition I like to use is it's kind of like a simplified perfect gas. The analogy is that when we talked about forces and drew free body diagrams, it didn't matter whether it was a plane or a train or a car or whatever. We drew everything as boxes because it was the simplest model for an object. And similarly, the simplest model for a gas is called an ideal gas. Now it basically just satisfies a couple of conditions here, and I want to go over them real quickly because you may need to know for a conceptual question on a homework or test. So let's get started. The first one is the gas has a low density. So what happens is that the particles in a container are going to be kind of spread out doing their own thing. They're not going to be super, super tightly crammed in together. So generally, what this means is that the pressure is pretty low, but the temperature is pretty high. You won't see any extreme values or anything like that. The second condition is that there are no forces between the gas particles. So in real life, in real gases, you have particles that exert some forces on each other. These are usually, like, electromagnetic forces. And for an ideal gas, we just consider that they don't exist. The third condition is that the particles have zero physical size. And what this means is that we're going to just treat ideal gas particles like points. So you basically just treat them as tiny little balls that are moving. They're very, very tiny. You can treat them as point particles, whereas real gas molecules actually do take up space. But for an ideal gas, we just assume that it's 0. The last one is that the particles are moving in straight lines, and they collide elastically. This is the most important part here. So, basically, these tiny little balls or these tiny little points are moving around. They move in perfectly straight lines until they collide with either the walls of the container or even each other. They can bounce off of each other. However, when they do collide, they collide elastically. And what that means is the energy in the container is conserved. There's no energy loss because these things are bumping around into each other. Alright. So what you really need to know about everyday conditions and ideal gases is that, you know, even under everyday conditions like in our atmosphere and things like that, most real gases already behave very much like ideal gases. So, you know, we can still use this model for an ideal gas even when we talk about real gases like oxygen and nitrogen in our atmosphere. Alright. So let's get to the equation then.

So the equations that govern ideal gases are called the ideal gas law, and it relates 4 related variables. We have pressure, volume, temperature, and moles, which is the amount of substance for an ideal gas. And it actually works for any ideal gas. It doesn't matter what it is. Now there are 2 different versions of this, and you may see both of them. So I want to go over them. The first one is PV=nRT. If you've ever taken an introductory chemistry course or something like that, you may be pretty familiar with this one. The other one is PV=nk_{B}T, where N is a big N. The difference between them is that they both work for ideal gases, is that you'll use this equation whenever you have the number of moles of substance, and you'll use this one whenever you're asked to find or you're given the number of particles, in a gas. And these things actually have a pretty simple relationship between them. n=N∕N_{A} , where N_{A} is Avogadro's number, 6.02×1023.

There are 2 constants that you need to know in both of these equations. The first one is big R, and it's called the universal gas constant. It's sometimes called the ideal gas constant, and it's just this number here, 8.314 jo__u__l__e__s∕ mol∕ K__e__l__v__in. The other one is k_{B}. This k_{B} is called Boltzmann's constant, and it has a value 1.38×10−23. Now the last thing here is that we're working with absolute temperatures, not changes in temperature. So the temperature actually must be in Kelvin. That's really, really important. You have to plug in all your temperatures in Kelvin. And the very last thing I want to mention here is that this is something you might see in your problems. So something called STP. It's an acronym that stands for standard temperature and pressure. Basically, it's just a common set of conditions that's very much like what we experience here at Earth's surface, which is that the temperature is 0 degrees Celsius or 273 Kelvin, and the pressure is 1.01×105. This is basically just whenever you see STP, these are your numbers for temperature and pressure. Alright? So let's get to our example here, which is we're going to calculate the volume of exactly one mole of an ideal gas that is at STP. So we're going to use those conditions here. So we have STP, which means the temperature is 0 Celsius or 273 Kelvin. We also have that the pressure is 1.01×105, Pascals. Now if we have one mole of substance, that's n=1, we want to figure out what is the volume. So we have these 4 variables. Remember, they're all related using the ideal gas law. So which version are we going to use? Well, remember, we're given the number of moles of a substance, so that means we're going to use PV=nRT. So what happens here is that there are 5 variables. There are 5 letters in this equation, but one of them is a constant. So there's really only 4 variables you need to know. If you ever have 3, you can always figure out the other one. So we know what the pressure is, we know what the number of moles is, and we have the temperature. Remember, this is just a constant, so we can figure out what this volume is by just rearranging the equation. So what happens is this p goes to the other side like this and your v is going to be nRT∕p. So I'm just going to start plugging in. The 1 mole, we have 8.314, that's the gas constant. 273, that's the temperature, and then 1.01×105 pascals. So when you work this out, what you're going to get is 0.0224, and this is going to be meters cubed. Now there are also a couple of other volume conversions that you may need to know for these types of problems. One of them is that 1 centimeter cube is 1 milliliter, and then sort of if you work this out and you play around with the zeros, you'll figure out that 1 meter cubed is 1,000 liters. So one way you might see this number represented, 0.0224, is when they multiply it by this conversion factor, you're going to multiply by a 1000 liters divided by 1 meter cubed. Meters cubed cancels. You're going to get 22.4 liters, and that's the answer. Either one of these numbers will be the answer. And that's actually a really sort of special number here. So the idea here is that 1 mole of any ideal gas at STP, sort of at these special conditions, has a volume of exactly 22.4 liters. Notice how we didn't talk about what type of gas it is. All we had were these conditions. So what this means here is that any gas at STP, whether you have 1 mole, occupies this amount of space, and this is sometimes called the molar volume of a gas at STP. Alright. So, guys, that's it for this one. Let me know if you have any questions.