1.

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» Correct Answer - (a) 1 " " `(b) sqrt((8kT)/(pim))`


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