Explain Maxwell-Boltzmann distribution curves of molecular speeds and give the important conclusions. Discuss the effect of temperature on the distribution of molecular speeds.

Explanation

According to kinetic gas equation it was assumed that all the molecules in á gas have the same velocity. But it is not correct. When any two molecules collide exchange of energy takes place and "hence their velocities keep on changing. At any instant few molecules may have zero velocity, a few .. molecules may be at high velocities and some may be with low velocities.
The distribution of speeds between different molecules were worked out by Maxwell by applying probability considerations.
If one plots a graph between fraction of molecules `(Delta N )/(N )` vs velocity one gets distribution curve of the type

These curves are shown at different temperatures ` T_1 ,T_2 (T_1 lt T_2)`
The graph reveals that
1. There are no molecules with zero velocity and only very few molecules possess the highest velocity.
2. The velocities of most of the molecules lie near a mean value.
3. As the temperature of the gas is increased, the curve becomes more flattened and shifts towards higher velocity. It means that at higher temperature the number of molecules possessing higher velocities is more than at lower temperature.
The peak point corresponds to the most probable velocity. It is the velocity possessed by maximum number of molecules. The average velocity of the molecules is slightly higher than the most probable velocity. The RMS velocity is slightly higher than the average velocity.