reaches the speed m s - due to another collision. So in general once the gas molecules attain equilibrium, the number of molecules that lie in the range of v to v+dv is always fixed. Note DEGREES OF FREEDOM . .
Definition The minimum number of independent coordinates needed to specify the position and configuration of a thermo-dynamical system in space is called the degree of freedom of the system. To know the number of molecules in the range of speed between m s − and m s − , we need to integrate π π N kT v e dv mv kT