The purpose of this work is to obtain a more precise calculation of the effective limits to the efficiency, of several cyclic heat engines. This calculation is based, first, on the equations describing the irreversible efficiency, and second, on a method which results from a general criterion to maximize this efficiency, applicable to several heat engines. With this method, we apply the criterion to maximize efficiencies; establish lower and upper bounds, corresponding to the efficiencies of Curzon–Ahlborn-like and Carnot-like heat engines; and, finally, find analytical or numerical expressions for the efficiencies ηme and ηmax. ηmax is the maximum irreversible efficiency; ηme is the efficiency in which the irreversible efficiency achieves its maximum, in a similar way to the Curzon–Ahlborn efficiency (maximum work or power). The method was applied to a Brayton cycle, presenting internal dissipations of the working fluid and irreversibilities due to the finite-rate heat transfer between the heat engine and its reservoirs. Also, we applied this method to a Carnot cycle including the irreversibilities of a finite-rate heat transfer between the heat engine and its reservoirs, heat leak between the reservoirs, and internal dissipations of the working fluid. The results obtained for the Brayton cycle are more general and useful than those in the relevant literature.

In this work we include, for the Carnot cycle, irreversibilities of linear finite rate of heat transfers between the heat engine and its reservoirs, heat leak between the reservoirs and internal dissipations of the working fluid. A first optimization of the power output, the efficiency and ecological function of an irreversible Carnot cycle, with respect to: internal temperature ratio, time ratio for the heat exchange and the allocation ratio of the heat exchangers; is performed. For the second and third optimizations, the optimum values for the time ratio and internal temperature ratio are substituted into the equation of power and, then, the optimizations with respect to the cost and effectiveness ratio of the heat exchangers are performed. Finally, a criterion of partial optimization for the class of irreversible Carnot engines is herein presented.

The concept of the efficiency of a process is used to analyse various thermodynamic power cycles with ideal gases. The Otto cycle is treated by considering irreversibilities coming exclusively from expansion and compression processes. For this cycle, the maximum irreversible work and the maximum efficiency are obtained in terms of the isentropic efficiencies and of the maximum and minimum temperatures of the reversible cycle. The results obtained are easily applicable to the Brayton cycle and have some similarities with those obtained from finite-time thermodynamics. The expression found for the efficiency of the Otto cycle for irreversible maximum work is similar to that obtained by maximizing the irreversible work in the Curzon-Ahlborn-Nokivov engine.

A stationary Carnot-like power plant model, with three sources of irreversibilities (the finite rate of heat transfers, heat leak and internal dissipations of the working fluid), is analyzed by a criterion of partial optimization for five objective functions (power, efficiency, ecological function, efficient power and criterion). A remarkable result is that if two constraints (design rules) are applied alternatively: constrained internal thermal conductance or fixed total area of the heat exchangers from hot and cold sides; the optimal allocation, cost and effectiveness of the heat exchangers are the same for all these objective functions independently of the transfer heat law used. Thus, it is enough to find these optimal relations for only one, maximum power, when all heat transfers are linear. In particular, for the Curzon–Albhorn-like model (without heat leak), the criterion for the so-called ecological function, including other variables (the internal isentropic temperature ratio), becomes total.