Physic Labs
problems.proof.stepOf
problems.proof.prevStepproblems.proof.nextStep
vx2‾=vy2‾=vz2‾=13v2‾ ⇒ pV=13Nmv2‾\overline{v_x^2} = \overline{v_y^2} = \overline{v_z^2} = \tfrac13\overline{v^2} \ \Rightarrow\ pV = \tfrac13 Nm\overline{v^2}
problems.proof.analysis

Since molecular motion is chaotic with no preferred direction, the mean square velocity splits evenly among the three directions: each gets 1/31/3 of v2‾=vx2‾+vy2‾+vz2‾\overline{v^2} = \overline{v_x^2}+\overline{v_y^2}+\overline{v_z^2}.