The other half of the principle of heat-work conversion cycles: The theorem, principle and core physical quantity of reversed cycles

Abstract

Engineering thermodynamics mainly focuses on the principles and methods for the heat-work conversion and to improve heat-work conversion efficiency. In current literatures, discussions are mainly focused on the heat-work cycles, which converts heat to work. Besides, the core physical quantity of heat-work cycles is entropy, which presents the heat-work conversion ability of the system. As for reversed cycles, the discussions are not quite detailed, and most of them applied the theory for heat-work cycles directly on reversed cycles. However, its well known that heat cannot be fully converted to work in a reversible thermodynamic cycle, which leads an efficiency less than 1. For reversed cycles, the heat output from the cycle can be much more than the net work the cycle costs, which derives a coefficient of performance (COP) more than 1. This phenomenon implies the principles of heat-work conversion in ordinary heat-work cycles and reversed cycles are somehow different, and some problems are naturally drawn as follows: (1) Is the COP of the reversed Carnot cycle the maximum possible COP for all reversed cycles within two temperature limits? (2) Heat can be judged from its quality, i.e. its temperature, and does the mechanical work have its quality? To answer these questions, this work analyzed and discussed the theorem, principle, and core physical quantity of reversed thermodynamic cycles. First, the principle for ordinary thermodynamic cycles are briefly reviewed, including the Carnot theorem and its proof, and the derivation of the concept of entropy from the Clausius original approach. Second, current conclusions of reversed cycles are reviewed and the air compression refrigeration cycle is taken as an example. The analysis comparing two cycles within given temperature limits presented that for given two temperature limits, the COP of the reversed Carnot cycle is the minimum possible COP, which is different from current conclusions. The quality of volumetric work is then discussed, and a new reversed cycle named reversed p-V cycle is proposed, which operates between two given pressure limits. The analysis indicates that this cycle is the best reversed cycle operating between two given pressure limits. Based on these discussion, the theorem and principle for reversed cycles corresponding to the second law and the Carnots theorem are derived and proved using the Clausius approach. The performance of the newly proposed reversed p-V cycle is investigated and compared with the reversed Carnot cycle operating within the same temperature limits, and results present that the COP of the reversed p-V cycle is much higher than the COP of the reversed Carnot cycle within the same temperature limits. Finally, from the equation of an arbitrary reversed cycle, it can be seen that the volume has a similar physical interpretation in the reversed cycles to the entropy in thermodynamic cycles, and it can be named as the work-entropy. In summary, the reversed cycles are analyzed, and its theorem, principles and core physical quantity are investigated.