Let consider only one molecule of a gas moving in a rectangular container. Assuming the collision is elastic, only the `x` component of the molecule's momentum changes. `∆P = mv_x - (-mv_x) = 2mv_x` `=>` Time between 2 collisions: `∆t = (2L)/v_x` Then we get Now let consider huge numbers (N) of molecules of gas moving in a rectangular container, and the average velocity of these molecules is `overline(v)`. velocity is a 2D vector `vec(v) = v_xvec(i) + v_xvec(j) +v_zvec(k)` the magnitude of `v = sqrt(v_x^2 +v_y^2+ v_z^2)` or `v^2 = v_x^2 +v_y^2+ v_z^2` Since average velocity `overline(v)` is an average of a huge number. `overline(v_x) = overline(v_y) =overline(v_z)`. we get: `v^2 = 3v_x^2` or `v_x^2 = 1/3 v^2`