We will now study what the velocity of the gas molecules is as a
function of the temperature. First we introduce the average squared
velocity <v^{2}>. This is obtained by taking the square
of the velocities of each molecule in the gas and averaging
(indicated by the angular brackets). One can show that in this case
<v^{2}> =
<v>^{2}.

The relationship between pressure, volume, and average velocity square is:

Here N is the number of molecules in the volume V, and m is the mass of one of them. Combining this result with the ideal gas law gives:

In the simulation, a hot gas (represented by red balls) is mixed with a cold gas (represented by the blue balls). As time passes, the gases interact with each other and reach equilibrium.