The first law of thermodynamics in hydrodynamic steady and unsteady flows
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| author | Giżyński, Konrad Makuch, Karol Paczesny, Jan Żuk, Paweł Maciołek, Anna Hołyst, Robert |
| author_facet | Giżyński, Konrad Makuch, Karol Paczesny, Jan Żuk, Paweł Maciołek, Anna Hołyst, Robert |
| contents | We studied planar compressible flows of ideal gas as models of a non-equilibrium thermodynamic system. We demonstrate that internal energy $U(S^{*},V,N)$ of such systems in stationary and non-stationary states is the function of only three parameters of state, i.e. non-equilibrium entropy $S^{*}$, volume $V$ and number of particles $N$ in the system. Upon transition between different states, the system obeys the first thermodynamic law, i.e. $dU=T^{*}dS^{*}-p^{*}dV+μ^{*}dN$, where $U=3/2 NRT^{*}$ and $p^{*}V=NRT^{*}$. Placing a cylinder inside the channel, we find that U depends on the location of the cylinder $y_{c}$ only via the parameters of state, i.e. $U(S^{*}(y_{c}),V,N(y_{c}))$ at V=const. Moreover, when the flow around the cylinder becomes unstable, and velocity, pressure, and density start to oscillate as a function of time, t, U depends on t only via the parameters of state, i.e. $U(S^{*}(t),V,N(t))$ for V=const. These examples show that such a form of internal energy is robust and does not depend on the particular boundary conditions even in the unsteady flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00463 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The first law of thermodynamics in hydrodynamic steady and unsteady flows Giżyński, Konrad Makuch, Karol Paczesny, Jan Żuk, Paweł Maciołek, Anna Hołyst, Robert Statistical Mechanics Fluid Dynamics We studied planar compressible flows of ideal gas as models of a non-equilibrium thermodynamic system. We demonstrate that internal energy $U(S^{*},V,N)$ of such systems in stationary and non-stationary states is the function of only three parameters of state, i.e. non-equilibrium entropy $S^{*}$, volume $V$ and number of particles $N$ in the system. Upon transition between different states, the system obeys the first thermodynamic law, i.e. $dU=T^{*}dS^{*}-p^{*}dV+μ^{*}dN$, where $U=3/2 NRT^{*}$ and $p^{*}V=NRT^{*}$. Placing a cylinder inside the channel, we find that U depends on the location of the cylinder $y_{c}$ only via the parameters of state, i.e. $U(S^{*}(y_{c}),V,N(y_{c}))$ at V=const. Moreover, when the flow around the cylinder becomes unstable, and velocity, pressure, and density start to oscillate as a function of time, t, U depends on t only via the parameters of state, i.e. $U(S^{*}(t),V,N(t))$ for V=const. These examples show that such a form of internal energy is robust and does not depend on the particular boundary conditions even in the unsteady flow. |
| title | The first law of thermodynamics in hydrodynamic steady and unsteady flows |
| topic | Statistical Mechanics Fluid Dynamics |
| url | https://arxiv.org/abs/2403.00463 |