Why is the Carnot Cycle the most efficient heat engine?

Desmond Sander asks:

You say: “There is no other heat engine that can convert heat to work more efficiently than the Carnot Cycle. It is the perfect heat engine.”

I ask: How about Rafa Nadal? Does he not convert the kinetic energy of the oxygen molecules he breathes (and other molecules in food) to the motions of his body which make him a great tennis player? Is that not a local increase in entropy, similar to the local increase in entropy that other individuals like you/me achieve so long as they are alive?



5 Replies to “Why is the Carnot Cycle the most efficient heat engine?”

  1. Mathematics has theorems, Physics has thought experiments. The Carnot Cycle is a thought experiment which uses the Ideal Gas Law  to compute the efficiency of a heat engine during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference by the application of work to the system. The important thing is that it is reversible; it operates sufficiently slowly for no heat to be lost to friction or turbulence. It describes either a heat engine or a refrigerator.

    Then why is it the most efficient thermodynamic cycle?

    Another thought experiment. Suppose a more efficient engine existed. Let it operate alongside a Carnot Engine working as a refrigerator between the same hot and cold reservoirs. Consider one cycle of the more efficient engine. An amount of heat, Q1, is lost from the hot reservoir, Q2 is delivered to the cold reservoir and work, W, where W = Q1 – Q2, is performed. Now suppose we use some of the work, Wc (where Wc < W), via the Carnot cycle refrigerator to move the same amount of heat, Q2, from the cold reservoir so that heat Wc+Q2 is delivered to the hot reservoir. The net effect is that cold reservoir is unchanged but W - Wc heat from the hot reservoir has been converted into work. This is against the Second Law of Thermodynamics because we have converted all the heat from a single reservoir into work. It is a perpetual motion machine of the second kind. It follows that the Carnot Cycle is the most efficient Thermodynamic Cycle.   The energy in the chemicals in Nadal's muscles was originally captured from solar radiation by photosynthesis. Carbohydrates molecules are more organized and have higher energy density and lower entropy than the H2O and CO2 molecules into which they break down. Entropy increases during physical exercise as in all exothermic chemical reactions.

  2. I would prefer to say that

    Mathematics has theorems, Physics has experiments, Science requires both.

    Thought experiments are not subject to the experimental testing that a Science requires. I think/say that makes the Carnot Cycle a compelling story, but no more than that. Whoever chose to call his Gas Law “Ideal” implicitly accepted this.

    A thought experiment is talk about an imagined/virtual world that some/many people —experts speaking truthfully and those who trust those experts — agree about. The talk we call Thermodynamics is compelling and locally useful, but that does not make it theTruth about theWorld. 

    Let me ask you now, whoever reads this, do you think that an alternative mathematical model/story of reality might work in which, for so long as he/she lives, each individual — in particular Rafa Nadal, in particular John Reid, in particular Greta Thunberg, in particular you, in particular me — actively changes what happens and what he/she says about it locally (in the time/place where he/she happens to be). In any such story, an individual human being describes and influences what happens locally as best he/she can, rather than passively accepting what is made to happen by the inexplicable forces of modern Mindless Physics. My Apple iBook 

    brain/mind — WHY THINKING WORKS 

    is a work in progress that presents such a model. It is the Physics of Life/Energy that I believe can and should replace the Physics of Objects/Forces that has been with us now for over two millennia.

    I think/say that

    “Carbohydrates molecules are more organized and have higher energy density and lower entropy than the H2O and CO2 molecules into which they break down”

    sounds sufficiently specific that it might these days be testable experimentally using sophisticated instruments which translate phenomena we humans cannot see into pictures we can see. On this I am very ignorant, and would like to know what people who use those instruments might have to say about experiments with molecules. Whoever does that will need to specify clearly what she/he means by “more organised” and other technical terms.

  3. The thought experiment outlined above outlines how, if the Carnot Cycle is not the most efficient cycle, one might go about constructing a perpetual motion machine. No one has yet done so, so the theory stands the test until someone does. That is how science works. I don’t know what is meant by “Truth about the World”. It sounds a bit religious.

    The entropy changes which occur during chemical reactions have been well understood for more than a century. See for example: http://www.shodor.org/unchem/advanced/thermo/index.html

  4. I think that any particular science, with its particular mathematics and particular physics is local to the place and time of whoever tells/believes that story. So long as a mathematics story is not experimentally falsified, its predictions are useful. So the mathematics of Euclid remains useful today for carpenters and architects, and the mathematics of Newton remains useful today for soldiers aiming howitzers.

    You say that “Truth about the World” sounds a bit religious. I guess this refers to my “theTruth about theWorld” which, spelled EXACTLY like that, is indeed intended to mock the priestly certainty that some/many scientists have about the stories they anoint as “theories”. If this blog allowed me to underline or italicise those terms theTruth and theWorld, as I do in my Apple iBooks, the mockery would be more apparent.

    I think that the human progress we call Science depends upon Mathematicians proving theorems and Physicists trying to falsify them. For this they need to be on the same page, so to speak. That’s my takeaway from Karl Popper, and it is the reason I’m here. I’ll say more about this, J, on your Blackjay site.

  5. I would agree with your first statement with the proviso that “local to the place and time” be replaced with “local to the scale” of the experiment or observation. The frequencies of hydrogen absorption lines observed in the laboratory have been precisely calculated using quantum mechanics. These same frequencies, proportionally red-shifted, are observed in the light from the most distant galaxies so this theory can hardly be described as local. The same quantum mechanics applies in furthemost reaches of the observed Universe as in the laboratory. On the other hand the mathematics of Euclid applies at the scales used by carpenters and architects. It does not apply at the scales used by cosmologists.

    I misunderstood the sense of your “Truth about the World” due to the fact that I have still not read your book (due to a certain close relative having forgotten to download it for me).

    Re “Mathematicians proving theorems”: replace “thought experiment” with “physics theorem” and that is more or less what I am saying. That the Carnot Cycle is the most efficient heat engine is such a theorem. If it should be shown to be incorrect by experiment it would have to be abandoned along with the Second Law of Thermodyanmics. So far this has not happened.

    The definition of “more organized” was precisely specified by Boltzmann, [TFC Equation (2.10)]. I am not a chemist and I don’t know how to apply it to chemistry but I presume that has been done. If not there’s a Nobel Prize in it for someone.

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