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Thermal Physics

Distribution of Molecular Speeds

Maxwell and Boltzmann used the kinetic theory to predict the distribution of speeds of molecules to be expected at a given temperature. They suggested that the number of molecules, N, which have speeds in a narrow range (from v to v + Dv) should give the following distribution.

vo corresponds to the "peak" of the curve, called the most probable speed.

vm is the mean (or average) speed of the molecules.

As the temperature of the gas increases, both the range of speeds and the mean (average) speed increases.

Therefore, for the same quantity of gas at a higher temperature the distribution is as shown by the red curve on the diagram below.

These predictions have been verified by experiment, thus giving support to the kinetic theory.

Some approximate average speeds (actually "root mean square" speeds) for molecules of different gases at different temperatures are given in the table below. The speeds are in ms-1.

Gas

at 273K

at 373K

H2

1·81×103

2·10×103

He

1·30×103

1·52×103

N2

4·90×102

5·73×102

You should be able to use any one of the lines in the table to show that temperature on the Kelvin scale is directly proportional to the average kinetic energy of the molecules.

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© David Hoult 2008