As part of the efforts to unify the various branches of Irreversible Thermodynamics, the proposed work reconsiders the approach of the Carnot engine taking into account the finite physical dimensions (heat transfer conductances) and the finite speed of the piston. The models introduce the irreversibility of the engine by two methods involving different constraints. The first method introduces the irreversibility by a so-called irreversibility ratio in the entropy balance applied to the cycle, while in the second method it is emphasized by the entropy generation rate. Various forms of heat transfer laws are analyzed, but most of the results are given for the case of the linear law. Also, individual cases are studied and reported in order to provide a simple analytical form of the results. The engine model developed allowed a formal optimization using the calculus of variations.

An irreversible Carnot cycle engine operating as a closed system is modeled using the Direct Method and the First Law of Thermodynamics for processes with Finite Speed. Several models considering the effect on the engine performance of external and internal irreversibilities expressed as a function of the piston speed are presented. External irreversibilities are due to heat transfer at temperature gradient between the cycle and heat reservoirs, while internal ones are represented by pressure losses due to the finite speed of the piston and friction. Moreover, a method for optimizing the temperature of the cycle fluid with respect to the temperature of source and sink and the piston speed is provided. The optimization results predict distinct maximums for the thermal efficiency and power output, as well as different behavior of the entropy generation per cycle and per time. The results obtained in this optimization, which is based on piston speed, and the Curzon–Ahlborn optimization, which is based on time duration, are compared and are found to differ significantly. Correction have been proposed in order to include internal irreversibility in the externally irreversible Carnot cycle from Curzon–Ahlborn optimization, which would be equivalent to a unification attempt of the two optimization analyses.

This paper presents the basic concepts and fundamental equations of the Thermodynamics with Finite Speed (TFS) resulted by the systematically study of the thermal reciprocating machine in relation with the piston finite speed and thermal molecular speed measured in the considered thermodynamic system. These concepts are based on the idea that any propagation of the interaction in the thermodynamic systems of finite dimensions is achieved by finite speeds: (1) - piston speed, (2) - average speed of the gas molecules inside the cylinder. A specific approach (scheme of calculation) for non-equilibrium (irreversible) thermodynamic processes is developed within TFS in order to find the fundamental equations appropriate for Optimizing Efficiency or COP and Power of thermal reciprocating machines. Analytical equations for all 5 irreversible thermodynamic processes in gases (isometric, isothermal, isobaric, adiabatic, polytropic) are deduced by integration of the combined First and Second Laws equation for processes with Finite Speed. This paper is limited to Irreversible Processes with Finite Speed, without taking into account the Friction and Throttling effects. It also notes the main moments in the development of TFS that led to these concepts and fundamental equations.