Gravitational Thermodynamics for Interstellar Gas and Weakly Degenerate Quantum Gas

The temperature distribution of an ideal gas in gravitational fields has been identified as a longstanding problem in thermodynamics and statistical physics. According to the principle of entropy increase (i.e., the principle of maximum entropy), we apply a variational principle to the thermodynamic...

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Bibliographic Details
Published in:Journal of the Physical Society of Japan 2016-03, Vol.85 (3), p.1-1
Main Authors: Zhu, Ding Yu, Shen, Jian Qi
Format: Article
Language:English
Subjects:
Density distribution
Entropy
Gases
Gravitation
Gravitational fields
Gravity
Ideal gas
Inhomogeneity
Quantum physics
Temperature distribution
Temperature gradient
Thermodynamics
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Summary:The temperature distribution of an ideal gas in gravitational fields has been identified as a longstanding problem in thermodynamics and statistical physics. According to the principle of entropy increase (i.e., the principle of maximum entropy), we apply a variational principle to the thermodynamical entropy functional of an ideal gas and establish a relationship between temperature gradient and gravitational field strength. As an illustrative example, the temperature and density distributions of an ideal gas in two simple but typical gravitational fields (i.e., a uniform gravitational field and an inverse-square gravitational field) are considered on the basis of entropic and hydrostatic equilibrium conditions. The effect of temperature inhomogeneity in gravitational fields is also addressed for a weakly degenerate quantum gas (e.g., Fermi and Bose gas). The present gravitational thermodynamics of a gas would have potential applications in quantum fluids, e.g., Bose-Einstein condensates in Earth's gravitational field and the temperature fluctuation spectrum in cosmic microwave background radiation.
ISSN:0031-9015
1347-4073