Lecture 03, concept 04: Deriving the Boltzmann distribution (a special case)

[@chemarun9941]

Outstanding performance und LECTURE

[@momchi98]

I absolutely adore this example. Thank you so much for showing it. It might be a special case, but it's such a down to Earth easy example that hints that the general form might be similar. For some reason when I studied statistical mechanics they taught it in the most convoluted way imaginable or just used it as an axiom, no motivation for the equation.

[@joenyc]

at 5:26, how did “p=F/A” become “p=force/volume”?

[@eriklindahl]

As I think I mentioned in the beginning, we're calculating/defining everything "per unit in the thin column" here, which effectively makes area the same as volume. As an interesting exercise, if you just explicitly include the cross-section of the column everywhere, you would eventually find that it cancels out. This is admittedly a bit sloppy, because it's only an initial illustration - the real generic derivation that doesn't make any assumptions about the system at all comes later in the class!