Maxwell distribution of kinetic energies

[bobwell]

Given that the average kinetic energy for molecules of an ideal gas is <E>=3/2kT, how can one find the percentage of molecules of the gas that contain energy above this value?

 

[Gerenuk]

I tried to solve the integral
- see http://en.wikipedia.org/wiki/Maxwell_distribution Equation 10
- you integrate from v=\sqrt{\frac{3kT}{m}} to infinity
- my result was
P(E &gt; 3/2\,kT)=\sqrt{\frac{6}{\pi e^3}}+\operatorname{erfc}\left(\sqrt{\frac{3}{2}}\right)=39.2\%
Feel free to check. (for integration use Mathematica, Matlab or for example "Tables of indefinite integrals" by Brychekov)