Temperature upper bound of an ideal gas
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911957587591168 |
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| author | Kim, Hyeong-Chan |
| author_facet | Kim, Hyeong-Chan |
| contents | We study thermodynamics of a heat-conducting ideal gas system. The study is based on i) the first law of thermodynamics from action formulation which expects heat-dependence of energy density and ii) the existence condition of a (local) Lorentz boost between an Eckart observer and a Landau-Lifshitz observer--a condition that extends the stability criterion of thermal equilibrium. The implications of these conditions include: i) Heat contributes to the energy density through the combination $q/nΘ^2$ where $q$, $n$, and $Θ$ represent heat, the number density, and the temperature, respectively. ii) The energy density has a unique minimum at $q=0$. iii) The temperature upper bound suppresses the heat dependence of the energy density inverse quadratically. This result explains why the expected heat dependence is difficult to observe in ordinary situation thermodynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_06994 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Temperature upper bound of an ideal gas Kim, Hyeong-Chan Statistical Mechanics General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics We study thermodynamics of a heat-conducting ideal gas system. The study is based on i) the first law of thermodynamics from action formulation which expects heat-dependence of energy density and ii) the existence condition of a (local) Lorentz boost between an Eckart observer and a Landau-Lifshitz observer--a condition that extends the stability criterion of thermal equilibrium. The implications of these conditions include: i) Heat contributes to the energy density through the combination $q/nΘ^2$ where $q$, $n$, and $Θ$ represent heat, the number density, and the temperature, respectively. ii) The energy density has a unique minimum at $q=0$. iii) The temperature upper bound suppresses the heat dependence of the energy density inverse quadratically. This result explains why the expected heat dependence is difficult to observe in ordinary situation thermodynamics. |
| title | Temperature upper bound of an ideal gas |
| topic | Statistical Mechanics General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2311.06994 |