The only option that comes to mind is a cycle with two transformations where the second one is just the first one but it's done backwards. Are there any other options?
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3 Answers
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Is it possible to have a thermodynamic cycle with zero work?
Yes. Any cycle where the positive work done equals the negative work done gives a net work of zero. An example is shown below that does not involve a cycle consisting of simply reversing a single process.
Positive work is the sum of the two areas under to two constant pressure expansion processes. Negative work is the area under under the single constant pressure compression processes. Select the equilibrium states such that the two areas are equal.
Hope this helps.
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Hmm, I think it's possible to have a zero work done in a thermodynamic process except what you said ...
W=-PdV
Case 1 : Isochoric process Here dV = 0. Therefore W(Work done) =0.
Case 2: Adiabatic free expansion Here there is no external pressure against which expansion is done so W=0 again.
Hope these points clear your doubts.
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1$\begingroup$ OP specifically asked about a thermodynamic cycle, not just a thermodynamic process. $\endgroup$– marchCommented Sep 15, 2023 at 19:44
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Kelvin's postulate: any two-stage cycle that consists of a single reversible isothermal stage and a single isentropic (reversible adiabatic) stage has zero delivered work. From this axiom it is fairly easy to show that a cycle that consists of an arbitrary number of isothermal stages of the same temperature interlaced with the same number of isentropic stages also delivers zero work.
answered Sep 15, 2023 at 18:55