The Principle of Least Action for Reversible Thermodynamic Processes and Cycles
The principle of least action, which is usually applied to natural phenomena, can also be used in optimization problems with manual intervention. Following a brief introduction to the brachistochrone problem in classical mechanics, the principle of least action was applied to the optimization of rev...
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| Format: | Article |
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MDPI AG
2018-07-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/20/7/542 |
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| author | Tian Zhao Yu-Chao Hua Zeng-Yuan Guo |
| author_facet | Tian Zhao Yu-Chao Hua Zeng-Yuan Guo |
| author_sort | Tian Zhao |
| collection | DOAJ |
| description | The principle of least action, which is usually applied to natural phenomena, can also be used in optimization problems with manual intervention. Following a brief introduction to the brachistochrone problem in classical mechanics, the principle of least action was applied to the optimization of reversible thermodynamic processes and cycles in this study. Analyses indicated that the entropy variation per unit of heat exchanged is the mode of action for reversible heat absorption or heat release processes. Minimizing this action led to the optimization of heat absorption or heat release processes, and the corresponding optimal path was the first or second half of a Carnot cycle. Finally, the action of an entire reversible thermodynamic cycle was determined as the sum of the actions of the heat absorption and release processes. Minimizing this action led to a Carnot cycle. This implies that the Carnot cycle can also be derived using the principle of least action derived from the entropy concept. |
| first_indexed | 2024-04-11T22:28:04Z |
| format | Article |
| id | doaj.art-0f37616d43774a818d30e56a5f829ee0 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T22:28:04Z |
| publishDate | 2018-07-01 |
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| record_format | Article |
| series | Entropy |
| spelling | doaj.art-0f37616d43774a818d30e56a5f829ee02022-12-22T03:59:35ZengMDPI AGEntropy1099-43002018-07-0120754210.3390/e20070542e20070542The Principle of Least Action for Reversible Thermodynamic Processes and CyclesTian Zhao0Yu-Chao Hua1Zeng-Yuan Guo2Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, ChinaKey Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, ChinaKey Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, ChinaThe principle of least action, which is usually applied to natural phenomena, can also be used in optimization problems with manual intervention. Following a brief introduction to the brachistochrone problem in classical mechanics, the principle of least action was applied to the optimization of reversible thermodynamic processes and cycles in this study. Analyses indicated that the entropy variation per unit of heat exchanged is the mode of action for reversible heat absorption or heat release processes. Minimizing this action led to the optimization of heat absorption or heat release processes, and the corresponding optimal path was the first or second half of a Carnot cycle. Finally, the action of an entire reversible thermodynamic cycle was determined as the sum of the actions of the heat absorption and release processes. Minimizing this action led to a Carnot cycle. This implies that the Carnot cycle can also be derived using the principle of least action derived from the entropy concept.http://www.mdpi.com/1099-4300/20/7/542principle of least actionoptimization problemsreversible thermodynamic processesCarnot cycle |
| spellingShingle | Tian Zhao Yu-Chao Hua Zeng-Yuan Guo The Principle of Least Action for Reversible Thermodynamic Processes and Cycles Entropy principle of least action optimization problems reversible thermodynamic processes Carnot cycle |
| title | The Principle of Least Action for Reversible Thermodynamic Processes and Cycles |
| title_full | The Principle of Least Action for Reversible Thermodynamic Processes and Cycles |
| title_fullStr | The Principle of Least Action for Reversible Thermodynamic Processes and Cycles |
| title_full_unstemmed | The Principle of Least Action for Reversible Thermodynamic Processes and Cycles |
| title_short | The Principle of Least Action for Reversible Thermodynamic Processes and Cycles |
| title_sort | principle of least action for reversible thermodynamic processes and cycles |
| topic | principle of least action optimization problems reversible thermodynamic processes Carnot cycle |
| url | http://www.mdpi.com/1099-4300/20/7/542 |
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