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Today I was tasked with correcting and grading a first year thermodynamics exam and one student drew a very peculiar diagram for the Ericsson-cycle. In the p-V-diagram the isothermal expansion and isothermal compression crossed. Now this is obviously wrong for the Ericcson-cycle, but can there be a thermodynamic cycle with crossings in the p-V-diagram? Is there a deeper reason why an internet search won't reveal any examples?

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  • $\begingroup$ Do you mean cross and continue on, or do you mean intersect and terminate at the point of intersection? $\endgroup$
    – Bob D
    Mar 6, 2020 at 19:09

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There is no physical reason why a cycle cannot cross in the diagram p-V diagram. However, there are practical reasons not to do that. Remember that the work done by the system in a cycle is the area inside the cycle in the p-v diagram. If a line cross, and you have something like a deformed eight (or two lobes), in one of the lobes the work will be positive but in the other it will be negative. You have both, a heating engine and a refrigerator in series. The cycle will be more efficient if you only keep one of the lobes instead.

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  • $\begingroup$ This is true in the case of a figure eight, but you could also have a cycle that crosses itself but where the work is positive in both subcycles. $\endgroup$ Mar 8, 2020 at 16:23
  • $\begingroup$ @EliasRiedelGårding True, I missed that. $\endgroup$
    – user65081
    Mar 8, 2020 at 17:09

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