## Thermal energy of a gas

If we have a gas with some heat, the atoms are all bouncing around and stuff. Their kinetic energy is

$KE = 1/2 m v^2$.

But momentum is given by $mv = p$, so we can rewrite the energy as

$KE = 1/2 pv$.

Everyone knows $pv = nRT$, so

$KE = 1/2 nRT$.

The kinetic energy of the motion of molecules is just the temperature of the gas!

(PS – this is a joke, but it actually gets the right answer for a 1-dimensional ideal gas. See wikipedia Thermal Energy)

### 2 Responses to “Thermal energy of a gas”

1. Rory Kent Says:

Aww, I was all done getting ‘angry commenter’ mind-set ready when I read the last line. I got troll’d.

Amusing to see that it works though. :D

2. Mark Eichenlaub Says:

Yesterday I asked a student to derive a formula for kinetic energy in terms of momentum and mass, eliminating velocity. When she was half way done I pointed this out as a joke, but she was pretty confused at first.