Molecular Level View
Let the length of the box the gas is in be Lx.
Since the gas molecule has to go back and forth to strike the area Ayz once, we have:
vx = 2Lx / ?t, or ?t = 2Lx/vx . Thus we get:
P*Ayz = 2mvx/ (2Lx/vx) = mvx2/Lx , or
P = mvx2/V where V = LxAyz , and so we have: P*V = mvx2 .