A cold region is maintained at the temperature TL below the environment temperature T0 by the steady operation of an irreversible refrigeration machine. The refrigeration load \dot{A_L} is attributed to the leakage of heat from T0 to TL. Prove that the total mechanical power demanded by this machine (\dot{W}) is equal to T0 times the total rate of entropy generation (\dot{S}gen), where (\dot{S}gen) equals the entropy generated by the irreversible refrigeration and by the leakage of \dog{A_L} from T0 to TL.