Thermodynamics of stationary states of the ideal gas in a heat flow

Makuch, Karol and Hołyst, Robert and Maciołek, Anna and Zuk, Pawel (2022) Thermodynamics of stationary states of the ideal gas in a heat flow. Journal of Chemical Physics, 157 (19). ISSN 0021-9606

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There is a long-standing question as to whether and to what extent it is possible to describe nonequilibrium systems in stationary states in terms of global thermodynamic functions. The positive answers have been obtained only for isothermal systems or systems with small temperature differences. We formulate thermodynamics of the stationary states of the ideal gas subjected to heat flow in the form of the zeroth, first, and second law. Surprisingly, the formal structure of steady state thermodynamics is the same as in equilibrium thermodynamics. We rigorously show that U satisfies the following equation dU= T* dS* -pdV for a constant number of particles, irrespective of the shape of the container, boundary conditions, size of the system, or mode of heat transfer into the system. We calculate S* and T* explicitly. The theory selects stable nonequilibrium steady states in a multistable system of ideal gas subjected to volumetric heating. It reduces to equilibrium thermodynamics when heat flux goes to zero.

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Journal Article
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Journal of Chemical Physics
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Copyright 2022 American Institute of Physics. The following article appeared in Journal of Chemical Physics, 157 (19), 2022 and may be found at This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
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27 Feb 2023 15:10
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27 Feb 2023 15:10