# Can some one explain following formula for average impulse of a molecule in the derivation of Boltzmann–Gibbs distribution

Thus, the total average impulse contributed by a molecule with an $$x$$-component velocity ranging between $$v_x$$ and $$v_x+\mathrm dv_x$$, is given by $$2mv_x\cdot\frac{v_x\tau}{L_x}\cdot\sqrt{\frac{\alpha}{\pi}}e^{-\alpha v_x^2}\mathrm dv_x$$

where $$v_x$$ is velocity of particle, $$τ$$ is the time during which the collision occurs with the wall of container and $$L_x$$ is the length of wall of the container.

What effect does factor $$v_xτ/L_x$$ explain in the equation?

• Consult any standard text on Kinetic Theory of Gases. I'll recommend Loeb. – sbp Oct 12 at 9:59
• The formula looks totally wrong. And wtf is $L_x$? – Kostas Oct 12 at 11:16
• Actually, gas is assumed to be in container of dimensions $L_x$, $L_y$, and $L_z$. – Nasir Aziz Oct 13 at 7:00