So, Carnot engine is THE reversible engine operating on two reservoirs. No other engine can beat its efficiency on two reservoirs (eg. Otto cycle is not Carnot as it requires infinite number of reservoirs to pass through the isochoric step). It strikes me, however, that steps of a Carnot cycle are unique for every working substance that are considered in undergraduate thermal physics courses (rubber bands, ideal/vdW gases, extended wires).

Do there exist thermodynamic systems where there is more than one possible reversible cycle between two reservoirs? In other words, is there a system in which apart from a cycle which roughly corresponds to typical isothermal-adiabatic-isothermal-adiabatic (possibly with other state variables involved) there is some other way of performing a Carnot cycle?

  • $\begingroup$ I have a feeling, if there was another heat engine based on different principles, or a significant tweak to the Carnot cycle that still managed matched the ideal (non existent) Carnot cycle, then you would be required to study it :( There are lots of pdfs on alternative to Carnot cycle, if you Google this phrase. $\endgroup$ – user175021 Nov 12 '17 at 9:00
  • $\begingroup$ The Carnot Cycle is by definition a process that takes place between two reservoirs connected by two adiabatic processes. It is not too difficult to prove that no thermodynamic cycle whose maximum and minimum operating temperatures are the same as a given Carnot Cycle can have higher efficiency than that of the Carnot cycle hence the primacy of the latter. See physics.stackexchange.com/questions/300347/… and physics.stackexchange.com/questions/200690/… $\endgroup$ – hyportnex Nov 12 '17 at 17:06

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