In kinetic theory of gas the velocity of molecules is expressed in the following three terms
(i) Root-mean square velocity or R.M.S. Velocity:
It may be defined as, “The square root of the mean value of the squares of the velocities of all molecules”. It is denoted by u. If are the velocities for n molecules, then
(ii) The average velocity is the arithmetic mean of the velocities of all molecules. It is denoted by v and is given by the following equation:
Average velocity (v) = 0.9213 x R. M. S. velocity (u)
(iii) The most probable velocity is the velocity possessed by maximum number of molecules of the gas at a given temperature. It is denoted by and is given by the following equation:
(since M= mN)
These three velocities are related to each other as:
Y : v : = 1.0 : 0.9213 : 0.8177
= 1.0 : 1.128 : 1.224 so
Maxwell’s distribution of velocities
Example 1: Calculate the root mean square velocity of nitrogen molecule at N.T.P.
Solution: According to kinetic gas equation:
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