On the Assumption of the Independence of Thermodynamic Properties on the Gravitational Field
A reversible cyclic process is analyzed in which the center of mass of an ideal gas is raised in a gravitational field during both an expansion phase and a subsequent contraction phase, with the gas returning to its initial height in a final step. When the properties of the gas are taken as uniform,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/7/930 |
| _version_ | 1817987269045256192 |
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| author | David S. Corti |
| author_facet | David S. Corti |
| author_sort | David S. Corti |
| collection | DOAJ |
| description | A reversible cyclic process is analyzed in which the center of mass of an ideal gas is raised in a gravitational field during both an expansion phase and a subsequent contraction phase, with the gas returning to its initial height in a final step. When the properties of the gas are taken as uniform, the thermodynamic efficiency of this cycle is able to exceed that of a corresponding Carnot cycle, which is a violation of the second law of thermodynamics. The source of this discrepancy was previously claimed, when analyzing a similar heating and cooling of a sphere, to be the assumed independence of the internal energy on the gravitational field. However, this violation is only apparent since all of the effects of the gravitational field were not incorporated fully into the thermodynamic analysis of the cycle. When all the influences of the gravitational field are considered, no possible violation of the second law can occur. The evaluation of the entropy changes of the gas throughout the cycle also highlights other key inconsistencies that arise when the full effects of the gravitational field are neglected. As the analysis of the cycle provided here shows, the assumption of the independence of the internal energy, as well as other thermodynamic properties, on the gravitational field strength can still be invoked. |
| first_indexed | 2024-04-14T00:19:53Z |
| format | Article |
| id | doaj.art-416c981b5d4b404caa598bc3d97ca625 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-14T00:19:53Z |
| publishDate | 2019-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-416c981b5d4b404caa598bc3d97ca6252022-12-22T02:23:00ZengMDPI AGSymmetry2073-89942019-07-0111793010.3390/sym11070930sym11070930On the Assumption of the Independence of Thermodynamic Properties on the Gravitational FieldDavid S. Corti0Davidson School of Chemical Engineering, Purdue University, 480 Stadium Mall Drive, West Lafayette, IN 47907-2100, USAA reversible cyclic process is analyzed in which the center of mass of an ideal gas is raised in a gravitational field during both an expansion phase and a subsequent contraction phase, with the gas returning to its initial height in a final step. When the properties of the gas are taken as uniform, the thermodynamic efficiency of this cycle is able to exceed that of a corresponding Carnot cycle, which is a violation of the second law of thermodynamics. The source of this discrepancy was previously claimed, when analyzing a similar heating and cooling of a sphere, to be the assumed independence of the internal energy on the gravitational field. However, this violation is only apparent since all of the effects of the gravitational field were not incorporated fully into the thermodynamic analysis of the cycle. When all the influences of the gravitational field are considered, no possible violation of the second law can occur. The evaluation of the entropy changes of the gas throughout the cycle also highlights other key inconsistencies that arise when the full effects of the gravitational field are neglected. As the analysis of the cycle provided here shows, the assumption of the independence of the internal energy, as well as other thermodynamic properties, on the gravitational field strength can still be invoked.https://www.mdpi.com/2073-8994/11/7/930thermodynamicsentropygravitational fieldsecond law of thermodynamics |
| spellingShingle | David S. Corti On the Assumption of the Independence of Thermodynamic Properties on the Gravitational Field Symmetry thermodynamics entropy gravitational field second law of thermodynamics |
| title | On the Assumption of the Independence of Thermodynamic Properties on the Gravitational Field |
| title_full | On the Assumption of the Independence of Thermodynamic Properties on the Gravitational Field |
| title_fullStr | On the Assumption of the Independence of Thermodynamic Properties on the Gravitational Field |
| title_full_unstemmed | On the Assumption of the Independence of Thermodynamic Properties on the Gravitational Field |
| title_short | On the Assumption of the Independence of Thermodynamic Properties on the Gravitational Field |
| title_sort | on the assumption of the independence of thermodynamic properties on the gravitational field |
| topic | thermodynamics entropy gravitational field second law of thermodynamics |
| url | https://www.mdpi.com/2073-8994/11/7/930 |
| work_keys_str_mv | AT davidscorti ontheassumptionoftheindependenceofthermodynamicpropertiesonthegravitationalfield |