Maxwell's Distribution pf Molecular Speeds

Maxwell showed using statistcal mechanics that the distribution of the speeds of the molecules of an ideal gas has a characteristic shape, shown in the graph below forat several temperatures.

As the temperature increases the graph moves to the right in smooth way, keeping a characterisitc shape.

There are three important measures of molecular speed, shown on the graph above. These are

The most probable speed,

The mean speed,

The root mean square speed,

The relationship between the three speed is given by the ratioThis ratio isor 1: 1.13:1.23. This ratio is constant because it does not depend on temperature.