So it turns out that each mode of motion of the atoms

contains on average one-half KT of energy.

So this is actually how the temperature is defined.

This T is the temperature.

K is the Boltzmann constant.

It's just a number you can look up in a book that doesn't change.

So if you have a gas that consists of single atoms,

not in molecules like argon is single atoms in the air,

that thing is flying around in space, and

because there are three dimensions of physical

space it turns out that a single atom gas like this will

tend to have three-halves KT of energy, one for

each of the three dimensions of physical space.

And then, if you have a molecule like oxygen,

one of the main gasses in our atmosphere, O2 has two atoms and

these two atoms can vibrate relative to each other.

And so, that vibration sets up another mode of

motion that the molecule can carry heat.

And the fact that it's now sort of a line instead of a point

means that it can rotate, as well.

And there are two different dimensions of rotation of this,

so you get two rotational modes from this atom, as well.