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I have been reading Feyman Lectures Volume 1 and I am stuck on the example or proof given in the book about how no machine can be more efficient than a reversible machine.

http://www.feynmanlectures.caltech.edu/I_04.html

Section 4-2

A very simple weight-lifting machine lifts weights three units “strong.” We place three units on one balance pan, and one unit on the other. However, in order to get it actually to work, we must lift a little weight off the left pan. On the other hand, we could lift a one-unit weight by lowering the three-unit weight, if we cheat a little by lifting a little weight off the other pan. Of course, we realize that with any

We imagine that there are two classes of machines, those that are

http://www.feynmanlectures.caltech.edu/I_04.html

Section 4-2

A very simple weight-lifting machine lifts weights three units “strong.” We place three units on one balance pan, and one unit on the other. However, in order to get it actually to work, we must lift a little weight off the left pan. On the other hand, we could lift a one-unit weight by lowering the three-unit weight, if we cheat a little by lifting a little weight off the other pan. Of course, we realize that with any

*actual*lifting machine, we must add a little extra to get it to run. This we disregard,*temporarily*. Ideal machines, although they do not exist, do not require anything extra. A machine that we actually use can be, in a sense,*almost*reversible: that is, if it will lift the weight of three by lowering a weight of one, then it will also lift nearly the weight of one the same amount by lowering the weight of three.We imagine that there are two classes of machines, those that are

*not*reversible, which includes all real machines, and those that*are*reversible, which of course are actually not attainable no matter how careful we may be in our design of bearings, levers, etc. We suppose, however, that there is such a thing—a reversible machine—which lowers one unit of weight (a pound or any other unit) by one unit of distance, and at the same time lifts a three-unit weight. Call this reversible machine, Machine A. Suppose this particular reversible machine lifts the three-unit weight a distance X. Then suppose we have another machine, Machine B, which is not necessarily reversible, which also lowers a unit weight a unit distance, but which lifts three units a distance Y We can now prove that Yis not higher than X, that is, it is impossible to build a machine that will lift a weight*any higher*than it will be lifted by a reversible machine. Let us see why. Let us suppose that Y were higher than X. We take a one-unit weight and lower it one unit height with Machine B, and that lifts the three-unit weight up a distance Y. Then we could lower the weight from Y to X*obtaining free power*, and use the reversible Machine A, running backwards, to lower the three-unit weight a distance X and lift the one-unit weight by one unit height. This will put the one-unit weight back where it was before, and leave both machines ready to be used again! We would therefore have perpetual motion if Y were higher than X, which we assumed was impossible. With those assumptions, we thus deduce that Y*is not higher than*X so that of all machines that can be designed, the reversible machine is the best.
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