Yeah lol, lots of physics and math was invented by multidisciplinary geniuses who saw equations that seemed to have no answer and said “oh yeah, this looks like a problem from biology that I’ve seen solved with this bit of fluid mechanics, and that problem can be solved with this complex trick from differential calculus. And you know, after we do that the whole system is starting to look like a circuit that uses properties from thermodynamics…”
Then your teacher and the textbook throws it on a white board and says “some smart dude figured out this was the way to solve this problem. It looks like this and it boils down to this equation. Don’t ask questions.”
…and then we take the partial derivative of the log of this infinite sum wrt molar volume to find that–
- Why?
Why what?
- helplessly gestures at the whiteboard
Oh, yeah, it’s so the math works out later! Anyway, for small Θ, the derivative has a nice closed form that we can Tailor expand in f-
Yeah lol, lots of physics and math was invented by multidisciplinary geniuses who saw equations that seemed to have no answer and said “oh yeah, this looks like a problem from biology that I’ve seen solved with this bit of fluid mechanics, and that problem can be solved with this complex trick from differential calculus. And you know, after we do that the whole system is starting to look like a circuit that uses properties from thermodynamics…”
Then your teacher and the textbook throws it on a white board and says “some smart dude figured out this was the way to solve this problem. It looks like this and it boils down to this equation. Don’t ask questions.”