Reversibility of the Work Curve requires no extra energy

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Mixed definitions of reversibility.

Reversibility is used in multiple senses.

Reversibility is a poorly defined property. Rather than argue which is right, here are the two types:

The Carnot/Kelvin reversibility measurements require conservation of energy and vice versa.

Other operations are described as irreversible when they almost always occur in one direction. Put a drop of colored liquid in water, the color rapidly disperses. Each molecule of color could migrate back to one spot, but the odds are (much) against it.

A word from the author. I was taught (Rice University) that any diffusion was irreversible. This is not the case. Case in point, a European company makes a car powered by compressed air. During compression, the energy of compression is diffused into the air. When driving the air powered car, the bottle is continuously reheated by the heat from the atmosphere. Complete reversal of diffusion, using the atmosphere as a near perfect energy storage. More on how to reverse diffusion on later pages in this chapter. MIT as of 2013 taught irreversibility has to do with whether something spontaneously happens or not. Respectfully, this is not Kelvin's definition, nor IMHO can anything happen which is not spontaneous. The fact that two prestigious Universities give completely unrelated explanations of Reversibility indicates grasping at straws, and pulling out different straw.

 

Reversibility per Carnot and Kelvin

In "Reflections" Both Sadi Carnot and Lord Kelvin refer extensively to steam engines, including their property of reversibility, state the property exists for all vapors, and by comparison very briefly touch on the Carnot Cycle. Lord Kelvin (not Carnot) goes further to propose a theorem that states (paraphrased) there can be no engine producing more work for a given amount of heat, because that would amount to creation of energy. (In depth in Theorems Chapter ) This theorem by Lord Kelvin's appears to be the basis for Carnot Theorems 1 and 2, citing the Carnot Cycle as uniquely reversible, when in "Reflections" Lord Kelvin is clearly speaking in broad brush, Steam Engines included. Kelvin used the phrase "it is readily seen that it is applicable to any conceivable kind of thermodynamic engine". The "Carnot Theorem" concludes roughly the opposite of Sadi Carnot's comments on reversibility being ubiquitous and Lord Kelvin's theorems as stated in "Reflections".

"Reflections" defines reversibility as the observed property of vapors in their heat engine experiments. This required energy to be conserved. Moving forward and back on either volume driven curve, heat driven curve, or any combination always results in the same path forward and reversed. This is evidence for the First Law, and almost certainly started the movement in science that resulted in the First Law decades later.

Newton died a generation before Carnot did his work. It seems obvious in hindsight, but absent, for "Reflections" to have drawn the correlation of Work = Pressure * Volume to Newton's Laws of Motion, Work = Force * Distance, which were complete and well known by this time. But now we have the benefit of a great deal of history and hindsight. We will never know why this was not in Carnot's or Kelvin's work on motion of engines. See chapter Newton for parallels.