Carnot cycle and theorem are major contributions of classical thermodynamics since proposed in 1824, while Carnot failed to prove it because of the influence of Caloric theory of heat. Then in 1850, Clausius confirmed Carnot theorem via reduction to absurdity and put forward the second law of thermodynamics. From then on, the theory that Carnot cycle is the one with the highest efficiency is generally accepted by scholars and regarded as the key premise or basis of thermodynamic analysis. However, few researchers care about how Carnot proposed the theory with the absence of the second law of thermodynamics. Can we get and prove Carnot theorem without the help of the second law of thermodynamics? In this paper, based on the polytropic process equations and p-v diagram, an analytical method of thermodynamics is developed and the cycle with the highest efficiency is deduced out only through extremum principle, instead of the second law of thermodynamics. The preliminary results indicate that Carnot cycle just serves as one form of the best cycles and only if the polytropic exponents (n) of the expansion and compression processes equal to each other, the efficiency of that cycle reaches the highest value, just that of Carnot cycle. This work gives a new insight into Carnot theorem and classical thermodynamics, which is of great importance in enlightenment for applying the new analysis method to address the complicated problems which are very difficult to address by using the second law of thermodynamics.
Shang, R., Zheng, Y., Shi, W., Wang, X., & Zhang, Y. (2014). Fresh look and understanding on carnot cycle. In Energy Procedia (Vol. 61, pp. 2898–2901). Elsevier Ltd. https://doi.org/10.1016/j.egypro.2014.12.213