<i>C</i>-<i>P</i> Diagram: A new thermodynamic analysis tool characterizing thermal cycles through geometric symmetry

<p>Traditional thermodynamic cycle analysis diagrams primarily emphasize basic thermodynamic parameters or energy flows, often overlooking the inherent symmetry of these cycles, a fundamental yet underutilized characteristic. This paper introduces a newly proposed <i>C</i>-<i>P</i> diagram, a graphical method that incorporates symmetry into thermodynamic cycle analysis and offers several key advantages. First, it provides a deeper insights into the underlying principles of thermodynamic cycles. Second, the use of symmetric geometric shapes enhances the analytical intuitiveness. Third, it shifts the analytical focus from isolated components to a holistic system-wide perspective. While conceptually akin to entropy-based methods for analyzing heat-to-work conversion cycles, the <i>C</i>-<i>P</i> diagram is broadly applicable, not only to heat transfer processes but also to work-producing cycles. This paper explores a wide range of applications of the <i>C</i>-<i>P</i> diagram, such as the analysis of exergy, irreversible process, finite-time thermodynamics, and multi-process coupling. Unlike traditional diagrams, which are often qualitative, the <i>C</i>-<i>P</i> diagram enables quantitative and concise graphical analysis. By visualizing exergy through symmetrical and simplified forms, it helps clarify complex phenomena such as the asymmetry of the maximum power output of real Brayton cycles. Moreover, the <i>C</i>-<i>P</i> diagram allows for the calculation of maximum power output and efficiency under finite heat transfer conditions using geometric relationships, and reveals interdependencies among component losses in coupled processes. As a supplement to conventional diagrams and also a novel framework rooted in symmetry and geometry, the <i>C</i>-<i>P</i> diagram represents a significant advancement in the analysis and optimization of thermodynamic systems.</p>