General Physics II

N_V, the Maxwell-Boltzman distribution function, describes the distribution of molecular speeds observed in a gas at some temperature T. N is the total number of molecules. N_v dv is the number of molecules found to have speeds between v and v + dv. We can also express these ideas in terms of probability. N_v dv/N is the probability of finding a molecule with speed between v and v + dv.

This Maxwell-Boltzman distribution function is given by

With this description of the speed distribution, we also find the following values:

v_rms is the "root mean square" value of the speed,

<v> is the average value or the mean value of the speed (of course, the mean value of the velocity is zero!),

And v_mp is the most probable value. The speed distribution curve has a maximum for v = v_mp,

This graph shows the Maxwell-Boltzman distribution function for two different temperatures.

Kinetic Theory of Gases

Distribution of Molecular Speeds