The Maxwell-Boltzmann distribution of molecular speeds in a sample of an ideal gas can be
Channel: Doubtnut
Date: 2020-02-16

The Maxwell-Boltzmann distribution of molecular speeds in a sample of an ideal gas can be expressed as `f=(4)/(sqrt(pi))((m)/(2kT))^(3//2)v^(2)e^(-(mv^(2))/(2kT)).dv` Where f represent the fraction of total molecules that have speeds between v and v + dv.m, k and T are mass of each molecule, Boltzmann constant and temperature of the gas. (a) What will be value of `overset(v=oo)underset(v=0)intfdv ?` (b) It is given that `overset(oo)underset(0)int v^(3)e^(-av^(2))dv=(1)/(2a^(2))` Find the average speed of gas molecules at temperature T.