Maxwell's Distribution

The distribution of speeds in an ideal gas is an interesting function of temperature. This is called Maxwell's distribution, or the Maxwell-Boltzmann distribution. James Clerk Maxwell showed that the probability of finding a molecule of a particular speed v is given by:
P(v) = 4π (
M
2πRT
) 3/2 v2 e-Mv2/2RT

M is the molar mass (mass of 1 mole) of the gas.

The distribution is characterized by three speeds. These are:
The root-mean-square speed:   vrms = (
3RT
M
) ½
The average speed:   vav = (
8RT
πM
) ½
The most probable speed:   vprob = (
2RT
M
) ½