Summary: Symmetry analysis is a cutting-edge research approach in physics, yet its application in macroscopic energy systems remains limited. This study demonstrates its potential to provide valuable insights for a deeper understanding and development of thermodynamic cycles. This article first studies the symmetry of the proposed C-P diagrams and finds rich symmetries including reflection symmetry, translation symmetry, and rotational symmetry within Carnot cycles. Then, it emphasizes that one can use symmetry alone to prove that the highest efficiency for any cycle operating in a certain temperature range is the Carnot efficiency, without relying on the entropy concept in the second law of thermodynamics. Lastly, it is found that this symmetry analysis framework can also be used for thermal cycles with phase transitions, as exemplified by applying in Rankine cycles. This research not only contributes groundbreaking insights into unraveling the symmetry inherent in thermodynamic cycles, but also promotes symmetry analysis to be an alternative analysis mean.
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