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.

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The paper presents the Fundamental Concepts, Equations and Diagrams in a new domain which is the extension of Thermodynamics with Finite Speed (TFS), invented and called by us: Quantum Biological Thermodynamics with Finite Speed of the Cardio-Pulmonary System (QBTFSCPS). The new concepts are: Stationary States, parameters of Stationary States, Processes between Stationary States with or without Quantum Jump, Non-Stationary States. Essential parameters of the Stationary States are: Frequency of Heart Oscillations FH, Frequency of Lungs Oscillations FL and Quantum Number N - which characterize the Synergetic (ordered) Interaction between Heart and Lungs, in a Stationary State. We present also a Fundamental Equation discovered by us, based on experimental data, which describes any Stationary States and 4 Equations of the Processes between these States in the Cardio-Pulmonary System. Based on these new concepts and new equations we invented 6 Diagrams which describe graphically in synoptic images the Stationary States and Processes between them with or Without Quantum Jump, between Quantum levels represented by the Quantum Number N (an integer number = 0, 1, 2, 3, 4, 5, 6, � etc.).

The paper presents the results of the recent studies and research conducted within the Quantum Biological Thermodynamics with Finite Speed on the calculation and interpretation of the Cardio-Pulmonary System performance. Thus, based on the new PV/Px diagram developed for the Cardio-Respiratory System, an original Scheme for calculating the Mechanical Work and Power of the Heart/Lungs has been developed. The new Calculation Scheme allows to study the variation of the Heart and Lungs parameters for each person, in Quantum States and in Processes with and without Quantum Jump. Based on the values calculated in each Stationary State, for the cases studied, the diagrams of the Mechanical Work, of the total Power and the Entropy Source for the Cardio-Pulmonary System, as functions of the Frequencies of the Heart (FH), and the Lungs (FL), the maximum systolic pressure and body mass of the person were thus constructed. The study and interpretation of these diagrams - which are novel elements - provides information on interactions within the Cardio-Pulmonary System or between it and the entire body, particularly useful in bioengineering for optimized and personalized design of artificial organs.