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In the Carnot cycle the original state is restored so there is no overall change in entropy. Why is it not possible to accomplish this simply with two reversible isothermal steps, the first an expansion and the second a contraction? In other words, why are the adiabatic steps necessary for restoration of the original state of the system?

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Well, Carnot cycle is intended for building an engine of very high work efficiency. If you neglect the adiabatic processes, it's completely possible to return into the original system, but what's the use as there is no work done? I will add a graph for you to understand better:

picture courtesy: google

Here the area between the points 1,2,3 and 4 are your work done. While building an engine, you certainly aim for some work done, don't you? But if you neglect the adiabatic processes the work done will be zero.

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  • $\begingroup$ Yes that's clearly the case... there would be no area under the curve and so no work. If we just did the first isotherm (1 to 2) by itself there would in fact be work but the system would not return to its original state and so could not run as an engine. $\endgroup$ – David Rosen Jan 8 '18 at 16:29

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