Considerations About The Anomalous Efficiency Of Particular Thermodynamic Cycles

Some years ago Vignati (refs. 1, 2, 3) showed that, under some particular circumstances (inter alia : isobaric processes connected through internal heat exchangers), the efficiency of an Ericsson cycle involving a real gas can exceed the Carnot limit ηC , in contradiction with the second principle of thermodynamics. However, the convergence of Vignati’s algorithm, giving the temperature difference between the intermediate heat exchangers, has not yet been proved. In particular, it isn’t clear, if the number of intermediate heat exchangers infinitely increases, the condition of a total (perfect) heat recovery may be asymptotically approximated. This remark is relevant because the claimed anomalous efficiencies appear only in the limit of a perfect heat recovery. Considering a suitable counterexample, we prove that, in general, the residual heat discharged on the external sources does not vanish in that limit, even when the isobars exchange the same amount of heat. Therefore the violation of the second law inferred from Vignati’s calculation is merely apparent, being referred to a situation which is not (in principle) physically realisable. The essentials of the Vignati’s argument are then applied to an Ericsson cycle involving an ideal gas undergoing chemical reactions. Again, no contradiction arises with the second principle. c © Electronic Journal of Theoretical Physics. All rights reserved.