Editors note
Originally entropy was not planned to be listed in this body of work. It has no part in Conservation of Energy, much less Conservation of Momentum, which is all that is needed to prove all engines will behave in a way to conserve energy (in fact the specific form of momentum).
The research this work is based on goes back to the original authors of engine science. They do not define or use the concept of Entropy, nor do they need to. All of their arguments and conclusions (that are viewed as valid today) can be shown as true by nothing more than Conservation of Momentum and Newton's laws of motion. Constant momentum is all that is needed to arrive at the conclusion that the only physical limit on any heat to or from motion transformation is 100%. Conservation of Energy requires the more general to be true as well.
A proof-reader, a physics student, asked the question. "What does Entropy have to do with it?" A legitimate question, for which I do not have a definitive answer. I can say Entropy is not required to calulate the outcome or efficiency of any engine cycle.
Many heat engine processes approach 100% fuel efficiency, or exceed the temperature ratio limit aka "Carnot" Limit. Some processes, such as compressed air engines, with a "Carnot" Limit of 0, "proving" compressed air engines can not possibly work, nevertheless work.
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Entropy and Rectangles.
An early and admittedly distant memory is that one property of the Carnot Cycle is that is you plot it in a certain way in "Entropy" space, you get a rectangle.
Not all that surprising. If you plot it as a volume vs pressure graph on a log - log scale, with x and y scale the log of volume and log of presser, respectively, the Carnot cycle is a parallelogram. Do the same with log Volume vs Log Temperature, you get a parallelogram. with two horizontal sides. Pick the slanty bit as the "y axis", and wallah, you have a rectangle. Not all shapes can as readily be converted to a rectangle, but so what?
The "proof" of entropy still falls back to diffusion of heat being a loss. And that simply isn't true. Diffusion of heat OUT of an engine is a loss. Diffusion to a second, third or Nth constrained volume of vapor, Inside the engine, ready to do something useful with the energy, is no loss at all. Diffusion does not in itself cause energy loss. The Engine Design does, if it allows diffusion to uselessly discard heat. All such arguments presume a single volume engine, which is a false and myopic assumption.
So I wonder which came first? Was Entropy developed to prove a Carnot Cycle can be squashed into a rectangle? Or was Entropy developed first and someone notice this unsurprising fact and imbue it with significance which is unfounded? Lots of work has been done with Entropy, and the research done here does not address that. Even if Entropy began because someone were grasping at straws to make the Carnot Cycle somehow special, it would not disprove the usefulness of the concept.
I have come to doubt the notion that total Entropy can change. If Energy is constant, and Entropy relies on change in Energy to itself change, does not conservation of Energy require total Entropy to be constant?
Much of the "science" of Entropy treated heat and motion as two forms of energy, which we know is untrue. Also, many assumptions still used today, such as a cooler material is required for something to cool off, are also wrong. Any body not being constantly "heated" will cool itself. We just see few examples of that happening when wrapped in an atmosphere. All bodies constantly radiate photons which reduces their "temperature" or relative random motion. Even in a vacuum, if the vacuum is within the atmosphere, an insulated body is exposed to the radiated heat of the opposite side of the vacuum, generally ambient temperature. There are many processes that increase order and many that decrease order. Gravity and black body radiation both tend to move atoms to closer, "cooler" relative positions.
But each very cold body in the universe has a massive "heat" relative to some other body moving at unimaginable speeds, as bodies in the universe tend to do. So what do you measure Entropy with respect to? Isn't it also subject to a frame of reference? Why would it be the only measurable quantity independent of a frame of reference? I suggest it is not (independent). I have no compelling proof.
That "reversibility" is irrelevant to the discussion of efficiency, hopefully will tend to avoid the argument of who has the right notion of defining reversibility, the original authors, or current thinking? Lord Kelvin's "proof" that nothing can be better than reversible engines, equally proves nothing can be worse than reversible engines. So Reversible does not matter. Since Conservation of Energy rules, Reversibility can go back to quiet corners of the science library.
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