Kinetic Theory of Gases

Distribution of Molecular Speeds

N

_{V}, theMaxwell-Boltzman distributionfunction, 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 ofprobability. N_{v}dv/N is the probability of finding a molecule with speed between v and v + dv.

ThisMaxwell-Boltzman distributionfunction is given byWith 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 thevelocityiszero!),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.

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