- 2111.13095
**Rights statement:**Copyright 2022 American Institute of Physics. The following article appeared in Journal of Chemical Physics, 157 (19), 2022 and may be found at http://dx.doi.org/10.1063/5.0128074 This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.Accepted author manuscript, 648 KB, PDF document

Available under license: CC BY: Creative Commons Attribution 4.0 International License

- https://arxiv.org/pdf/2111.13095.pdf
Accepted author manuscript

- https://aip.scitation.org/doi/10.1063/5.0128074
Final published version

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published

In: Journal of Chemical Physics, Vol. 157, No. 19, 21.11.2022.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Makuch, K, Hołyst, R, Maciołek, A & Zuk, P 2022, 'Thermodynamics of stationary states of the ideal gas in a heat flow', *Journal of Chemical Physics*, vol. 157, no. 19. https://doi.org/10.1063/5.0128074

Makuch, K., Hołyst, R., Maciołek, A., & Zuk, P. (2022). Thermodynamics of stationary states of the ideal gas in a heat flow. *Journal of Chemical Physics*, *157*(19). https://doi.org/10.1063/5.0128074

Makuch K, Hołyst R, Maciołek A, Zuk P. Thermodynamics of stationary states of the ideal gas in a heat flow. Journal of Chemical Physics. 2022 Nov 21;157(19). doi: 10.1063/5.0128074

@article{948c2425ea254ea3926e5cfdbd4f83a3,

title = "Thermodynamics of stationary states of the ideal gas in a heat flow",

abstract = "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.",

keywords = "General Physics and Astronomy, Physical and Theoretical Chemistry",

author = "Karol Makuch and Robert Ho{\l}yst and Anna Macio{\l}ek and Pawel Zuk",

note = "Copyright 2022 American Institute of Physics. The following article appeared in Journal of Chemical Physics, 157 (19), 2022 and may be found at http://dx.doi.org/10.1063/5.0128074 This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. ",

year = "2022",

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T1 - Thermodynamics of stationary states of the ideal gas in a heat flow

AU - Makuch, Karol

AU - Hołyst, Robert

AU - Maciołek, Anna

AU - Zuk, Pawel

N1 - Copyright 2022 American Institute of Physics. The following article appeared in Journal of Chemical Physics, 157 (19), 2022 and may be found at http://dx.doi.org/10.1063/5.0128074 This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

PY - 2022/11/21

Y1 - 2022/11/21

N2 - 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.

AB - 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.

KW - General Physics and Astronomy

KW - Physical and Theoretical Chemistry

U2 - 10.1063/5.0128074

DO - 10.1063/5.0128074

M3 - Journal article

VL - 157

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 19

ER -