Thermodynamic techniques used to analyze and optimize irreversible cycles involve mainly both the exergy model, i.e. second law efficiency, and the entropy generation minimization [1]. This paper presents an appraising comprehensive direct method based on two overall numbers of irreversibility, external and internal ones. These two numbers link the first and second laws of Thermodynamics inside the first law efficiency, called in this paper the irreversible first law efficiency. The number of external irreversibility is the ratio of second law effectiveness of the cycle external heat exchanges, which were set up by relating the real heat exchange of the working fluid with external heat reservoirs, to the ideal completely reversible one, assuming both a heat transfer area tending to infinity and a heat transfer temperature difference tending to zero. The number of internal irreversibility manages the irreversible entropy production along the cycle. This paper includes selected numerical results regarding the internal irreversibility connected to the nature of the working fluid in a Joule-Brayton engine cycle.

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