Molecules in a certain Speed Range

To calculate the number of molecules with speeds in certain range, it is necessary to integrate the speed distribution function between the limits of that range (Fig 4.17). The number of molecules having speeds between 0 and v is given by

Fig.4.17 Number of Molecules in the speed range of 0 and v

(4.121)

Let ,                                and  then on substitution,

(4.122)

Integrating by parts,

(4.123)