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[Phys-L] kinetic energy +- inconsistencies



Hi --

If we look at the classical microscopic physics of an ideal
gas, 100% of the energy is kinetic energy.

OTOH if we put the gas in a cylinder, and take the macroscopic
position of the piston as the only coordinate of interest,
then the gas acts like a spring, giving rise to a potential
energy.

So which is it, KE or PE? Well, it depends on the choice
of coordinates. The professional physicist knows how to
tiptoe through this minefield, but students don't.

The specific context almost doesn't matter, but if
you're curious, here it is:
http://www.av8n.com/physics/degeneracy.htm
See especially question 1 and question 13.

I mention this because I recently got called on it: A student
had his own way of thinking about KE+PE which was different
from mine, and wanted to know why his way was wrong. His
way surprised me and confused me, but it wasn't wrong. (My
way wasn't wrong either.)

I was impressed, because one of the foundations of critical
reasoning is /cross-checking/ to see in what ways each new
idea is consistent (or inconsistent!) with previously-known
ideas. When students catch this kind of inconsistency it's
a good sign; it means they are paying attention.

To say the same thing the other way, it's kinda depressing
how many people accept the simple explanation without noticing
that it is inconsistent with other ways of using the same
ideas. And it's not because they have figured out how to
resolve the inconsistencies; they just gloss over them.

Pedagogically this is tricky, and I'm not nearly as good
at it as I'd like to be. If I point out the connections
and/or inconsistencies occasionally, that's OK, especially
at first ... but if I do it every time, it defeats the
purpose. The goal is to get the students to do it on
their own, all day every day.