Physic Labs
problems.proof.intuition

Exactly like a tennis ball hitting a wall and bouncing back at the same speed — the wall receives exactly twice the ball's original momentum.

Δpper collision=2mvx\Delta p_{\text{per collision}} = 2mv_x
problems.proof.analysis

Consider a molecule of mass mm with velocity component vxv_x perpendicular to the wall, undergoing an elastic collision (bouncing back at the same speed). Its momentum changes from mvxmv_x to −mvx-mv_x, so the momentum delivered to the wall is 2mvx2mv_x.