Deriving Boltzmann's Constant

This is one of those really simple things that is still really cool to learn.
Starting from the ideal gas law..

Where P is the pressure, V is the volume, n is the number of kilomoles there are, R is the gas constant and T is the temperature.

We will first start by dividing by Avogadro's number and assume we have one kilo-mole of gas. (Meaning n=1)

So the energy per-unit molecule is E=kT.