 You might, I assume that you've heard of gas laws and everything before, and you probably also know that the velocities of molecules somehow corresponds to temperature. If we increase the temperature, molecules will, on average, move faster. So there is a classical relation behind that. If we draw an x, y diagram here, where we have on the x diagram, I say speed. So basically the absolute value of velocity. And here we say, let's say density or the number of molecules. At low temperature, say 300 Kelvin or something, the maximum here is gonna be fairly sharp and occur at fairly low temperatures. So let's say that's 300 Kelvin. Now, if I bump up the temperature a little bit, on average, the molecules will move faster, but it does not mean that each and every molecule will move, say, 10 meters per second faster or something. But we're gonna have a slightly different distribution. And even in this case, there will be some molecules that move very slowly. So maybe it would look like this. And now I'm just inventing numbers here. Let's say 500 Kelvin. And finally, if you really crank up the heater here, move up to 700 Kelvin, we might have something like this. Again, these are purely for illustration. So how do we determine this? Well, this is the so-called Maxwell-Boltzmann velocity distribution. So it's related to a Boltzmann. It was Maxwell using Boltzmann's results to describe how this influences gases. And ultimately, this is what's described where we have different pressures in gases and everything as a function of temperature. But this is just an illustration. It does not explain why this happened. And as the next concept in the class, we're gonna need to go in and start deriving this. Why do things on average move faster at 700 Kelvin? Because here too, it's a matter of energy, right? We know that the kinetic energy of a molecule is the kinetic energy Eken of a small particle that is equal to the mass of the particles multiplied by the velocity squared divided by two. There is no question that that V is higher at 700 than at 500, sorry, that V is higher further up here, right? So in principle, if we wanted to go after low Eken, all of them should be at zero. So why is it that not all of them are at zero and why is that that depends also on the temperature? So there is something here where the temperature influences molecules ability to stick to different velocities. Next up, we're gonna derive that.