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 `int_(v=0)^(v=oo)fdv ?`
(b) It is given that `int_(0)^(oo) v^(3)e^(-av^(2))dv=(1)/(2a^(2))`
Find the average speed of gas molecules at temperature T.

Answer

(a) 1 " " `(b) sqrt((8kT)/(pim))`