While
deriving Kinetic Gas Equation, it was assumed that all molecules in a gas have the same velocity. But it is not so. When any two molecules collide, one molecule transfers kinetic energy (mv²) to the other molecule. The velocity of the molecule which gains energy increases and that of the other decreases. Millions of such molecular collisions are taking place per second. Therefore, the velocities of molecules are changing constantly. Since the number of molecules is very large, a fraction of molecules will have the same particular velocity. In this way there is a broad distribution of velocities over different fractions of molecules. In 1860 James Clark Maxwell calculated the distribution of velocities from the laws of probability. He derived the following equation for the distribution of molecular velocities.
dN = number of molecules having velocities between C and (C+dc)
N = total number of molecules
M = molecular mass
T = temperature on absolute scale (K)
The relation stated above is called Maxwell's law of distribution of velocities. The ratio dn In gives the fraction of the total number of molecules having velocities between C and (C + dc). Maxwell plotted such fractions against velocity possessed by the molecules. The curves so obtained illustrate the salient features of Maxwell distribution of velocities.
(1) A very small fraction of molecules has either very low (close to zero) or very high velocities.
(2) Most intermediate fractions of molecules have velocities close to an average velocity represented by the peak of the curve. This velocity is called the most probable velocity. It may be defined as the velocity possessed by the largest fraction of molecules corresponding to the highest point on the Maxvellian curve.
(3) At higher temperature, the whole curve shifts to the right (dotted curve at 600 K). This shows that at higher temperature more molecules have higher velocities and fewer molecules have lower velocities.
