# Fun With Maxwell Distribution

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?

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