Journal of Modern Physics, 2013, 4, 1-7 Published Online December 2013 (http://www.scirp.org/journal/jmp) http://dx.doi.org/10.4236/jmp.2013.412A2001 Open Access JMP On the Efficiency for Non-Endoreversible Stirling and Ericsson Cycles Delfino Ladino-Luna, Pedro Portillo-Díaz, Ricardo T. Páez-Hernández Universidad Autónoma Metropolitana-Azcapotzalco, Física de Procesos Irreversibles, México D.F., México Email: dll@correo.azc.uam.mx, pportillodaz@gmail.com, phrt@correo.azc.uam.mx Received October 1, 2013; revised November 2, 2013; accepted November 27, 2013 Copyright © 2013 Delfino Ladino-Luna et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ABSTRACT An analysis of the Stirling and Ericsson cycles from the point of view of the finite time thermodynamics is made by assuming the existence of internal irreversibilities in an engine modeled by these cycles, and the ideal gas as working substance is considered. Expressions of efficiency in both regimes maximum power output and maximum ecological function are also shown. Appropriate variables are introduced so that the objective functions, namely power output, ecological function and efficiency can be functions of the reservoirs temperatures ratio and certain “measurable” parameters as a thermal conductance, the general constant of gases and the compression ratio of the cycle. Several results from the finite time thermodynamics literature are used, so that the developed methodology leads directly to appropriate expressions of the objective functions in order to simplify the optimization process. Keywords: Thermal Cycles; Efficiency; Power Output; Ecological Function 1. Introduction As it is known, thermal engines can be assumed as en- dothermic or exothermic devices. Among the first, Otto and Diesel engines are the best known; and among the second two devices, Stirling and Ericsson engines are very interesting and similar to the theoretical Carnot en- gine [1,2]. They are engines closed-cycles regenerative devices initially used for various applications, particu- larly the Stirling cycle as water pumping and until the middle of last century manufactured on a large scale. But the development of the internal combustion engines from the mid-nineteenth century and the improvement in the refining of fossil fuels influenced the abandonment of the Stirling and the Ericsson engines in the race for industriali- zation, gradually since the early twentieth century. It is important to point out that Stirling and Ericsson cycles have an efficiency which goes towards the Carnot effi- ciency as it is shown in some textbooks. It is also important to point out that a difference be- tween endothermic and exothermic engines is the type of fuel used. While the first mentioned engines need fuel of a certain quality, the other engines can work with low- quality fuels and even alternative sources such as solar energy. Also in exothermic engines the working fluid does not change its composition during the cycle; these engines are quiet and safe but not very powerful. So, since the end of the previous century, and on recent times, Stirling and Ericsson engines characteristics have re- sulted in renewed interest in the study and design of such engines, and in the analysis of its theoretical idealized cycle, as it is shown in many papers [3-20]. Nevertheless, the discussion on these engines and its theoretical model has not been exhausted. On other hand, the finite time thermodynamics theory actually is considered an extension of the classical equi- librium thermodynamics in the study of heat engines, in which explicitly is included time dependence of heat transfer processes between reservoirs and engine [21-28]. By excluding the irreversible processes occurring within the working substance, it is obtained the endoreversible cycle, but if the effects of these internal irreversible proc- esses are took into account, the cycle is called non-en- doreversible. The exclusion of such effects is known as endoreversibility hypothesis, and is considered for cases in which the internal relaxation time of the working sub- stance is very small compared with the total cycle time. At first Curzon and Ahlborn analyzed the endoreversible Carnot cycle with finite heat transfer between hot and cold thermal reservoirs with temperatures H T T and C , H C T T  , and the engine. Ideal gas as working substance