Adding Heat Back to a Carnot Cycle Heat Engine

Q. I am a recently-retired rocket-propellant scientist. A friend of mine believes he has found a way of adding heat back to a Carnot Cycle heat engine so as to increase its efficiency above that predicted by the Second Law of Thermodynamics. Could you please give me some pointers so that I will be able to either prove him right or prove him wrong.

R. Do not attempt to prove your friend wrong or right. Friendship is about acceptance, respect and caring. You friend is making his contribution, whether it will become recognized or not, just by thinking about these things. Any efforts to prove your friend right or wrong are doomed to failure and disappointment and will probably cause you, and you friend, to feel frustrated and lonely. During his short life, Carnot’s masterpiece on the motive power of fire and machines for harnessing that power was not recognized by others as having any value. William Thomson, Lord Kelvin, later found the work and understood its significance. It contained the basis of the Second Law of Thermodynamics and the notion of a perfect machine: a reversible machine; one whose actions could be undone while leaving no trace whatsoever in its own state or in the net effects it had had on its surroundings. Sadi Carnot could have done with a friend — it seems he became very disillusioned after writing his treatise. He did not need someone to prove him right or wrong.

We know that, with current technology, we cannot expect to build Carnot’s perfect machine because of effects such as

The factors mentioned all give rise to practical difficulties in realising engines. However, knowing how substances behave from the results of experiments and knowing how machines follow fundamental physical laws that have been established, based on observation and experiment, we can predict with very high accuracy and very high confidence how an ideal machine would perform. If it is an ideal heat engine, we can predict its efficiency.

A thermal reservoir is a source or sink of heat transfer that always remains at the same temperature. Sadi Carnot proposed that all ideal engines that operate between the same two thermal reservoirs at fixed temperatures have the same thermal efficiency. He also proposed that no engine could have a higher thermal efficiency than an ideal engine if it operated between the same two thermal reservoirs. These two parts of the general principle, known as Carnot’s Principle, encapsulate the Second Law of Thermodynamics.

Carnot’s principle can readily be generalized to include engines that receive heat transfer over a range of temperatures and reject heat over a (normally different) range of temperatures. The general conclusion, loosely stated, is that no engine can be more efficient than an ideal heat engine that receives and rejects heat transfer over the same temperature ranges as that engine.

Another formulation of the Second Law of Thermodynamics, which is due to Clausius, states that it is impossible for any device or system that undergoes no net change in its own state to cause heat transfer from a given thermal reservoir to another thermal reservoir at a higher temperature and to have no other net effect on the state of its surroundings. A heat engine may undergo changes in its state in the course of a cycle, but return to its initial state, thereby undergoing no net change in its state. A heat engine operating in reverse, such as a refrigerator, can cause heat transfer from a thermal reservoir to another thermal reservoir at a higher temperature. However, it does not violate the Clausius statement of the Second Law because it has another net effect on its surroundings: it takes a net work input.

There is no proof of Carnot’s Principle, or of the Second Law of Thermodynamics, other than myriads of observations that have been made by mankind. So far, from observations made on Earth and from observations made by astronomers looking out into the rest of the Universe, no phenomena have been discovered that would violate the Second Law of Thermodynamics.

Assuming that the generally accepted laws of mechanics and thermodynamics (not including the Second Law) are valid, it can be shown that Carnot’s principle is logically equivalent to the Clausius statement of the Second Law of Thermodynamics. There will be no need for your friend to build, or even design, an engine that can exceed the efficiency of an ideal Carnot type heat engine. An easier task to accomplish, and a sufficient objective, would be to demonstrate that there exists some system or machine that can, unaided and without undergoing any net change in its own state, bring about the transfer of heat from a system at any given tempertaure to a system at a higher temperature, no matter how slightly higher.

Of course, if your friend has found that one of the other generally accepted laws of mechanics and thermodynamics is invalid, you should encourage him to focus on demonstrating that invalidity, rather than complicating the issue through the involvement of heat engines. And always remember, you are your own friend too.

Leo Nest, ULFC

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