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### Perpetual Motion Machines

Modern instruction in engineering tends to focus on the things we can do: devices and processes that have been developed and put to good use. In contrast, little attention is given to things that we cannot do: devices that cannot function as intended. In fact, as an aid to learning, study of such devices can improve our understanding of the world and our place in it. Here we describe one class of devices that cannot function as advertised: perpetual motion machines.

When, in 1824, Sadi Carnot deduced what would later become the second law of thermodynamics, he started from the premise that it is impossible to construct a perpetual motion machine. When, in 1847, Hermann von Helmholtz formulated the modern statement of the first law, he too started from the premise that perpetual motion machines are impossible. Given these historical facts, it is somewhat disconcerting that today we appeal to the first and second laws to "prove" that perpetual motion machines are impossible.

By a perpetual motion machine we mean more than a device that runs forever under its own power. Rather we mean either (a) a cyclic device that does useful work without taking energy from its surroundings or (b) a cyclic device that produces more useful work than the total amount of energy it takes from its surroundings. Such (hypothetical) devices can be divided into three kinds.

## Perpetual Motion Machine of the First Kind

A perpetual motion machine of the first kind would operate by violating the first law of thermodynamics in the form of the mechanical energy balance. A traditional example is an overshot waterwheel, in which water falling over the wheel rotates a shaft. The potential energy given up by the falling water is converted into rotational kinetic energy at the shaft. Some of that kinetic energy is used to do useful work, such as to grind grain or to drive a generator of electricity. The rest of that kinetic energy would be used to pump the water back to the top of the wheel, so it could again help turn the shaft. Thus, the water forms a closed circuit.

The fallacy in this design is the assumption that the energy required to pump the water back to the top of the wheel is less than the amount extracted from the water as it falls over the wheel. In fact, the magnitudes of the potential energies associated with raising and lowering the water are exactly the same. Thus, no energy is left to do useful work. In practice the situation is actually worse for two reasons:

1. The energy obtained from the wheel is less than the change in potential energy of the falling water because some of that energy is wasted to friction at the shaft bearings.
2. The energy needed to pump the water back to the top is greater than the change in potential energy of the rising water because some of that energy must overcome friction in the pump.

Therefore, real water wheels operate in open systems in which new water is continually being supplied by a flowing river or stream.

## Perpetual Motion Machine of the Second Kind

Perpetual motion machines of the first kind would create energy from nothing; those of the second kind would not create energy but would convert, with 100% efficiency, energy from another form into work, and do so repeatedly in a cycle. Such devices violate the second law of thermodynamics.

The traditional example of a perpetual motion machine of the second kind is a heat engine operating at 100% efficiency. A heat engine takes energy in the form of heat and converts some of it into useful work; examples are steam plants for ships, locomotives, and electrical power generation. These devices are common, but they cannot operate at 100% efficiency; that is, they cannot convert all of the given heat into useful work: some must be expelled into the environment, usually to the atmosphere via cooling towers or into lakes and rivers via heat exchangers. Obviously, it would be economically and environmentally desirable to operate heat engines at 100% efficiency, but the second law assures us that this cannot be done.

## Perpetual Motion Machine of the Third Kind

These devices violate a general form of the first law that includes terms beyond those contained in the standard mechanical energy balance. Examples include terms that account for radiant, electrical, magnetic, nuclear, and other forms of energy.

Also included here are devices that violate the combined mass-energy conservation law. An example is a device that provides useful work from the heat generated by the decay of a radioisotope. The catch here is that the device must operate in a cycle; hence, at some point the mass of the radioisotope must be replenished from an external source. The device cannot supply useful work and maintain the mass of the radioisotope, for this would violate the law of conservation of mass-energy.

The development of Western technical culture is littered with fallacious ideas: geometers attempted to square the circle, alchemists attempted to transmute base metals into gold, engineers attempted to construct perpetual motion machines. But fallacious ideas are not necessarily bad ideas: we usually must take several wrong turns before we find the proper path. Afterwards, reconsiderations as to why certain turns were wrong can broaden and deepen our understandings, and such understandings may help us avoid some wrong turns in the future.