The Carnot Cycle, Reversibility and Entropy
The Carnot cycle and the attendant notions of reversibility and entropy are examined. It is shown how the modern view of these concepts still corresponds to the ideas Clausius laid down in the nineteenth century. As such, they reflect the outmoded idea, current at the time, that heat is motion. It i...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/7/810 |
| _version_ | 1827688786837897216 |
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| author | David Sands |
| author_facet | David Sands |
| author_sort | David Sands |
| collection | DOAJ |
| description | The Carnot cycle and the attendant notions of reversibility and entropy are examined. It is shown how the modern view of these concepts still corresponds to the ideas Clausius laid down in the nineteenth century. As such, they reflect the outmoded idea, current at the time, that heat is motion. It is shown how this view of heat led Clausius to develop the entropy of a body based on the work that could be performed in a reversible process rather than the work that is actually performed in an irreversible process. In consequence, Clausius built into entropy a conflict with energy conservation, which is concerned with actual changes in energy. In this paper, reversibility and irreversibility are investigated by means of a macroscopic formulation of internal mechanisms of damping based on rate equations for the distribution of energy within a gas. It is shown that work processes involving a step change in external pressure, however small, are intrinsically irreversible. However, under idealised conditions of zero damping the gas inside a piston expands and traces out a trajectory through the space of equilibrium states. Therefore, the entropy change due to heat flow from the reservoir matches the entropy change of the equilibrium states. This trajectory can be traced out in reverse as the piston reverses direction, but if the external conditions are adjusted appropriately, the gas can be made to trace out a Carnot cycle in P-V space. The cycle is dynamic as opposed to quasi-static as the piston has kinetic energy equal in difference to the work performed internally and externally. |
| first_indexed | 2024-03-10T10:03:33Z |
| format | Article |
| id | doaj.art-688682f83fb940958b728475123200ec |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T10:03:33Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-688682f83fb940958b728475123200ec2023-11-22T01:43:26ZengMDPI AGEntropy1099-43002021-06-0123781010.3390/e23070810The Carnot Cycle, Reversibility and EntropyDavid Sands0Department of Physics and Mathematics, University of Hull, Hull HU6 7RX, UKThe Carnot cycle and the attendant notions of reversibility and entropy are examined. It is shown how the modern view of these concepts still corresponds to the ideas Clausius laid down in the nineteenth century. As such, they reflect the outmoded idea, current at the time, that heat is motion. It is shown how this view of heat led Clausius to develop the entropy of a body based on the work that could be performed in a reversible process rather than the work that is actually performed in an irreversible process. In consequence, Clausius built into entropy a conflict with energy conservation, which is concerned with actual changes in energy. In this paper, reversibility and irreversibility are investigated by means of a macroscopic formulation of internal mechanisms of damping based on rate equations for the distribution of energy within a gas. It is shown that work processes involving a step change in external pressure, however small, are intrinsically irreversible. However, under idealised conditions of zero damping the gas inside a piston expands and traces out a trajectory through the space of equilibrium states. Therefore, the entropy change due to heat flow from the reservoir matches the entropy change of the equilibrium states. This trajectory can be traced out in reverse as the piston reverses direction, but if the external conditions are adjusted appropriately, the gas can be made to trace out a Carnot cycle in P-V space. The cycle is dynamic as opposed to quasi-static as the piston has kinetic energy equal in difference to the work performed internally and externally.https://www.mdpi.com/1099-4300/23/7/810Carnot cycleentropyreversibilityirreversibilityClausius |
| spellingShingle | David Sands The Carnot Cycle, Reversibility and Entropy Entropy Carnot cycle entropy reversibility irreversibility Clausius |
| title | The Carnot Cycle, Reversibility and Entropy |
| title_full | The Carnot Cycle, Reversibility and Entropy |
| title_fullStr | The Carnot Cycle, Reversibility and Entropy |
| title_full_unstemmed | The Carnot Cycle, Reversibility and Entropy |
| title_short | The Carnot Cycle, Reversibility and Entropy |
| title_sort | carnot cycle reversibility and entropy |
| topic | Carnot cycle entropy reversibility irreversibility Clausius |
| url | https://www.mdpi.com/1099-4300/23/7/810 |
| work_keys_str_mv | AT davidsands thecarnotcyclereversibilityandentropy AT davidsands carnotcyclereversibilityandentropy |