# Fun With Maxwell Distribution

**Classical Mechanics**Level 5

The Maxwell distribution describes the velocities of the molecules of an ideal gas at equilibrium. The probability for finding a molecule with velocities between \(\vec{v}\) and \(\vec{v}+d\vec{v}\) is given by
\[ dP=\left(\frac{m}{2\pi k T}\right)^{3/2} e^{-\frac{m v^{2}}{2 k T}} dv_{x} d v_{y} d v_{z} \quad \text{(Maxwell Distribution)}\]
where \(m\) is the mass of the molecules, \(k\) is the Boltzmann constant and T is the temperature of the gas. If the mean speed of the molecules of a gas is \(<v>=300~\text{m/s}\), what is the mean of the inverse of the speed \(<1/v>\) **in seconds per meter**?