The speed and energy of all the molecules of the gas at any instant are not the same. Thus, we can obtain only average value of speed of molecules. If there are n number of molecules in a sample and their individual speeds are u1 , u2 , …….un , then average speed of molecules uav = (u1 +u2 +u3+…. un)/ n

Maxwell and Boltzmann have shown that actual distribution of molecular speeds depends on temperature and molecular mass of a gas.

Maxwell and Boltzmann have shown that the distribution of molecular speeds

Molecular speed depends on the temperature and molecular mass of a gas.

Maxwell derived a formula for calculating the number of molecules possessing a particular speed.

The distribution of speeds shown in the plot is called the Maxwell-Boltzmann distribution of speeds.

Maxwell-Boltzmann distribution of speeds have shown that actual distribution of molecular speeds depends on temperature and molecular mass of a gas.

Maxwell-Boltzmann distribution of speeds shows that number of molecules possessing very high and very low speed is very small.

The maximum in the curve represents speed possessed by maximum number of molecules.

The speed possessed by maximum number of molecules is called most probable speed, ump. This is very close to the average speed of the molecules.

On increasing the temperature most probable speed increases. Also, speed distribution curve broadens at higher temperature.

At the same temperature, gas molecules with heavier mass have slower speed than lighter gas molecules. At the same temperature lighter nitrogen molecules move faster than heavier chlorine molecules. Hence, at any given temperature, nitrogen molecules have higher value of most probable speed than the chlorine molecules.

The mean square speed is the direct measure of the average kinetic energy of gas molecules. If we take the square root of the mean of the square of speeds then we get root mean square speed

Urms= (u12 +u22 +..........un2)/ n.

Root mean square speed, average speed and the most probable speed have following relationship: urms > uav > ump

The ratio between the three speeds is given below : ump : uav : urms : : 1 : 1.128 : 1.224