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Direction of Spontaneous Processes in Non-Equilibrium Systems with Movable/Permeable Internal Walls.

Robert Hołyst1, Paweł J Żuk1, Anna Maciołek1,2

  • 1Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warszawa, Poland.

Entropy (Basel, Switzerland)
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Summary

The second law of thermodynamics governs non-equilibrium systems, including gases in heat flow. This study extends thermodynamic principles to predict wall motion in various gas systems under non-equilibrium conditions.

Keywords:
entropygravitynon-equilibrium thermodynamicsstationary statesteady statethermodynamics

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Fluid Dynamics

Background:

  • Classical thermodynamics and the second law are well-established for equilibrium systems.
  • Non-equilibrium thermodynamics requires extensions to describe dynamic processes.
  • Understanding heat flow and particle interactions is crucial for complex systems.

Purpose of the Study:

  • To investigate the applicability of thermodynamic inequalities in non-equilibrium heat flow scenarios.
  • To analyze the direction of wall motion in various gas systems under non-equilibrium conditions.
  • To synthesize findings into a generalized framework for the second law of non-equilibrium thermodynamics.

Main Methods:

  • Analysis of heat flow in ideal gases, van der Waals gases, and binary mixtures.
  • Introduction of a movable internal wall to partition systems.
  • Application of thermodynamic inequalities (dU-đQ≤0 and dE-đQ-đWs≤0) to predict motion.
  • Inclusion of gravitational fields and permeable walls to derive Archimedes' principle.
  • Consideration of Couette (shear) flow for ideal gases.

Main Results:

  • The inequality dU-đQ≤0 determines wall motion direction in heat flow for ideal and van der Waals gases, and binary mixtures.
  • This inequality remains valid with gravitational fields and permeable walls, leading to Archimedes' principle in heat flow.
  • For Couette flow, the inequality dE-đQ-đWs≤0 governs wall motion.
  • A unified framework for the second law of non-equilibrium thermodynamics is established.

Conclusions:

  • The second law of thermodynamics can be extended to non-equilibrium systems involving heat flow.
  • Thermodynamic inequalities provide a consistent method for predicting system behavior under various non-equilibrium conditions.
  • This research unifies diverse non-equilibrium phenomena within a single theoretical structure.