Therefore, the loss of kinetic energy in all collisions per unit area and per unit time is:

(4.41)

If the area of the moving piston is A, the loss of the molecular K.E. in all collisions on the piston per unit time is

Rate at which work is done on the piston

(4.42)

It is thus proved that when a gas expands adiabatically against a moving piston, work is done at the expense of the K.E. of the molecules, and hence the temperature of the gas decreases.