 So how can you actually work out what this pressure is? Well, let's imagine we had some box containing a gas, and the box had some volume V, and the gas inside is at a temperature of T. And you want to work out what the pressure this gas applies to the inside of the box is. So let's look at a little tiny bit of the side of the box, some area A. We're going to get molecules bouncing off it. How much force are they going to apply? Well, we know the force is going to go up if the molecules are moving faster. If you can hit by something that's moving faster, it's going to hurt more. So that means you'd expect the force to be proportional to... Now this is a proportional to sign. That means we're not trying to work out exactly what the force is equal to, we're just trying to see what it depends on. So it's going to be proportional to, it's going to depend on the temperature. So if the temperature gets higher, that means the molecules are moving faster, so you expect the force to be bigger. So that means the force is proportional to temperature. As the temperature goes up, the force goes up. That sounds sensible. What else is it going to depend on? It's also going to depend on how many molecules are hitting the inside. If lots of molecules are hitting, that's going to give you a big pressure force, if only a small number, a small pressure force. So that's going to depend on the density of the molecules. If they're packed in close, more are going to be hitting. And density is equal to the number of molecules divided by the volume. That's like a million atoms or molecules in a volume of one square meter, the density of one million atoms per square meter, say. So let's give us the rough idea. It turns out that the exact formula for what's called an ideal gas is that the pressure force is equal to a constant times the density, the number density, that's the number of molecules per unit area, not the mass per unit area, which is number divided by volume, times the temperature. And k is a constant we've seen before. It's Boltzmann's constant, which is 1.38 by 10 to the minus 23 joules per Kelvin. This is called the ideal gas law. Now, what's an ideal gas? There is no such thing. An ideal gas is a gas where all the molecules don't hit each other, they only hit the walls, and they are perfectly elastic and they have no interaction with each other. No real gases like that, but most gases behave quite like this when they're fairly hot and they've got pretty low density. When they start getting thick and sludgy and high density, it doesn't work very well. But for things like air, fairly low density, reasonably warm, it actually works pretty well. We can rearrange it and we get the pressure times the volume equals the number of molecules in that volume times Boltzmann's constant times the temperature. So that's the normal form you see the ideal gas law written in. So what does this mean? Well, let's say you have a box of gas and you double the temperature. The volume remains the same, therefore the pressure must double. The temperature, by the way, must be measured in Kelvin. Or let's say this box is actually a cylinder with a piston and you push the piston in, so the volume shrinks in half. If the temperature remains same and the volume shrinks in half, the pressure must double to compensate. Which means that when you squash gas, it generally gets higher pressure, which is how a bicycle pump works. So this is the simplest form of the ideal gas law, and it works fairly well for most fairly low density gases.