Module 4 : Kinetic Theory of Gases

Lecture 6 : Applications of Maxwell-Boltzmann Distribution

(4.115)

or,

(4.116)

The most probable speed is the speed at which the largest number of molecules is moving. It is the speed which occurs most frequently. To determine vmp , the expression of  is differentiated with respect to v and equated to zero. From equation (4.105), using β,

(4.117)

or,

(4.118)

or,

(4.119)

The relative magnitudes of the three speeds are shown in Fig. 4.16 and their values are in the following proportions:

Fig.4.16 Relative magnitudes of vmp,  and vrpm

(4.120)