Perpetual Motion?

The answer is no; there is no perpetual motion machine. However, it did almost look possible to create such a thing as Carnot was developing his theories. This machine requires three things to be possible: an ideal heat machine could be made to run backwards, so that it took in work to "pump" heat from a hot reservoir to a cold reservoir; an ideal heat pump and an ideal heat engine could be hooked together so that they draw from and contribute to the same hot and cold heat reservoir; and that there can be variable amounts of work produced from an ideal heat engine using the same heat reservoirs. If the work required to drive the heat pump was less than the work given off by the heat engine (hence the need for a variable work output requirement for this thing to work), then using two differing heat reservoirs you could produce unlimited work.

Carnot was, however, a strong believer in the impossibility of perpetual motion, so he used this whole scenario as proof that there can be no variation in the work output of an ideal heat engine if the heat input Qh and the two reservoir temperatures Th and Tc are the same.

Incidentally, the "heat pump" that Carnot envisioned has a practical application: refrigerators. A refrigerator uses the expansion and compression of a gas to transfer heat away from the inside of the refrigerator and radiate it out to the surroundings. This expansion and compression of the gas requires work to proceed - so the whole process is the opposite of a heat engine.