The motive force of the Carnot engine operating at maximum power production

An existence theorem is proved for the motive force in the Carnot engine producing maximum power. The virial theorem is refined. The motive forces of the engine are expressed in terms of kinematic characteristics of the engine piston. It is shown that the process of isothermal expansion of the ideal gas obeys the "3/2" law establishing the dependence of the piston coordinate on time.