example_lecture.txt

Good afternoon. Nice weather today, isn't it? I'm thinking about visiting the lakefill later. Well, it's eleven so I suppose we should get started. Near the end of last class we began to discuss the Van der Waals equation and its differences from the Ideal Gas law that you most likely relied on in your high school chemistry days. Maybe general chem here... I don't know. Anyways, the Ideal Gas law does not sufficiently describe the world well enough for our applications. In fact, it is only "true" for inert gases at very low temperatures and pressures. But that's no fun, is it? We want to be able to describe situations more, more robustly than this. While Van der Waals is not entirely true to physics either, it is close enough that we can accurately judge a lot of properties and behaviors sufficiently, just about anything we will be covering in this course. So recall that we are now including these two parameters, so-called a and b, which have an effect on the equation of state. These parameters are intrinsic to a gas; they are calculated experimentally or derived from statistical mechanics. We will simply have to look them up, say for water vapor for example, in a table whenever we need to use them. I'm not expecting you to know exactly what these constants represent, but it's important to be able to think about them in the same sense as we've been treating other parameters. For example, if I could somehow increase b, the volume of the gas would need to decrease for the equation to hold at a constant temperature and pressure. In this way, we can better understand properties of the gas that might not be intuitively clear. As another example, we could consider Maxwell's relations. It is immediately clear from our manipulation that S is inverse to T, with all other parameters fixed. I don't know about you but I would not be able to see that without the help of these equations. We can also derive other facts from Van der Waals that are perhaps more useful and can't be given using only the Ideal Gas law. For example, if we consider the particles of the gas as packed spheres, which they very well might be, then we can calculate the radius of each particle of gas directly [inaudible] seemingly unrelated Van der Waals equation. Atkins is a bit lazy and gives the figure as 0.5 times b, but it's closer to 0.78, 0.79 times b or so. And this works remarkably well. For chlorine gas at STP, we get within an Angstrom.