{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:06:28Z","timestamp":1760058388394,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T00:00:00Z","timestamp":1743033600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>After a brief review of Carnot\u2019s everlasting contributions to the foundations of thermodynamics, we critically examine the consequences of the Carnot theorem, which leaves behind some lingering questions and confusion that persist even today. What is the one significant aspect of the Carnot cycle that leads to this theorem? When does the working substance play an important role for an engine and what is its correlation with the protocol\u00a0of operational details? Do all reversible engines working between the same two temperatures have the same maximum efficiency of the Carnot engine as Fermi has suggested? Are all heat engines equivalent to a Carnot engine in disguise? Our new perspective allows for the clarification of these questions with a positive answer for the last question. Recognizing that Carnot eventually abandoned the caloric theory, we use a result by Carnot and simple dimensional analysis to show how the first law, the concept of entropy, and the efficiency of the Carnot engine could have been germinated by Carnot in his time. This then demonstrates that Carnot had good understanding of entropy before its invention by Clausius. We suggest that both should be credited with inventing entropy by calling it Carnot\u2013Clausius entropy. We also clarify some fundamental misconceptions plaguing reversible regenerators and their irreversible replacement by heat exchangers in the field.<\/jats:p>","DOI":"10.3390\/e27040346","type":"journal-article","created":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T04:36:48Z","timestamp":1743136608000},"page":"346","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Carnot Theorem Revisited: A Critical Perspective"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4092-5062","authenticated-orcid":false,"given":"P. D.","family":"Gujrati","sequence":"first","affiliation":[{"name":"Department of Physics, The University of Akron, Akron, OH 44325, USA"},{"name":"School of Polymer Science and Polymer Engineering, The University of Akron, Akron, OH 44325, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,27]]},"reference":[{"key":"ref_1","unstructured":"Thurston, R.H. (1897). Reflections on the Motive Power of Heat, John Wiley & Sons. [2nd ed.]."},{"key":"ref_2","unstructured":"Clausius, R. (1879). The Mechanical Theory of Heat, Macmillan."},{"key":"ref_3","first-page":"61","article-title":"On the Mechanical Equivalent of Heat","volume":"140","author":"Joule","year":"1850","journal-title":"Philos. Trans. R. Soc. 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