Fourier’s Law in a Generalized Piston Model
A simplified, but non trivial, mechanical model—gas of N particles of mass m in a box partitioned by n mobile adiabatic walls of mass M—interacting with two thermal baths at different temperatures, is discussed in the framework of kinetic theory. Following an approach due to Smoluchowski, from an an...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-07-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/19/7/350 |
| _version_ | 1818001136503750656 |
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| author | Lorenzo Caprini Luca Cerino Alessandro Sarracino Angelo Vulpiani |
| author_facet | Lorenzo Caprini Luca Cerino Alessandro Sarracino Angelo Vulpiani |
| author_sort | Lorenzo Caprini |
| collection | DOAJ |
| description | A simplified, but non trivial, mechanical model—gas of N particles of mass m in a box partitioned by n mobile adiabatic walls of mass M—interacting with two thermal baths at different temperatures, is discussed in the framework of kinetic theory. Following an approach due to Smoluchowski, from an analysis of the collisions particles/walls, we derive the values of the main thermodynamic quantities for the stationary non-equilibrium states. The results are compared with extensive numerical simulations; in the limit of large n, m N / M ≫ 1 and m / M ≪ 1 , we find a good approximation of Fourier’s law. |
| first_indexed | 2024-04-14T03:30:43Z |
| format | Article |
| id | doaj.art-19595d50bce540b3867f153bba6db391 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T03:30:43Z |
| publishDate | 2017-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-19595d50bce540b3867f153bba6db3912022-12-22T02:14:58ZengMDPI AGEntropy1099-43002017-07-0119735010.3390/e19070350e19070350Fourier’s Law in a Generalized Piston ModelLorenzo Caprini0Luca Cerino1Alessandro Sarracino2Angelo Vulpiani3GSSI (Gran Sasso Science Institute), Università dell’Aquila, Viale Francesco Crispi, 7, 67100 L’Aquila, ItalyDipartimento di Fisica, Università di Roma Sapienza, P.le Aldo Moro 2, 00185 Rome, ItalyISC-CNR and Dipartimento di Fisica, Università di Roma Sapienza, P.le Aldo Moro 2, 00185 Rome, ItalyDipartimento di Fisica, Università di Roma Sapienza, P.le Aldo Moro 2, 00185 Rome, ItalyA simplified, but non trivial, mechanical model—gas of N particles of mass m in a box partitioned by n mobile adiabatic walls of mass M—interacting with two thermal baths at different temperatures, is discussed in the framework of kinetic theory. Following an approach due to Smoluchowski, from an analysis of the collisions particles/walls, we derive the values of the main thermodynamic quantities for the stationary non-equilibrium states. The results are compared with extensive numerical simulations; in the limit of large n, m N / M ≫ 1 and m / M ≪ 1 , we find a good approximation of Fourier’s law.https://www.mdpi.com/1099-4300/19/7/350Fourier’s lawkinetic theorynon equilibrium statistical mechanics |
| spellingShingle | Lorenzo Caprini Luca Cerino Alessandro Sarracino Angelo Vulpiani Fourier’s Law in a Generalized Piston Model Entropy Fourier’s law kinetic theory non equilibrium statistical mechanics |
| title | Fourier’s Law in a Generalized Piston Model |
| title_full | Fourier’s Law in a Generalized Piston Model |
| title_fullStr | Fourier’s Law in a Generalized Piston Model |
| title_full_unstemmed | Fourier’s Law in a Generalized Piston Model |
| title_short | Fourier’s Law in a Generalized Piston Model |
| title_sort | fourier s law in a generalized piston model |
| topic | Fourier’s law kinetic theory non equilibrium statistical mechanics |
| url | https://www.mdpi.com/1099-4300/19/7/350 |
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