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Boltzmann's Analysis of Macroscopic and Microscopic Aspects of Reversible Thermodynamic Processes

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This Demonstration considers three different reversible processes from both a macroscopic and a microscopic point of view: isothermal expansion and compression, isochoric heating and cooling, and adiabatic expansion and compression [1]. Select the process, then use the checkbox to choose between heating–expansion or cooling–compression.

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Use the "animate gas particle" button to start the animation. The temperature is indicated schematically on the color bar at the bottom.

At the top left is a pressure-volume plot for each process (isothermal in blue, isochoric in green and adiabatic in orange). Also shown are a piston and cylinder representing these processes. At the right is a schematic representation of the energy level distribution.

Global entropy is defined as the sum of the system entropy variation of the piston and the surrounding entropy variation . In a reversible processes .

When the system entropy change is positive, the entropy change of the surroundings must be negative, and vice versa. Both entropy changes are equal to 0 only in an adiabatic process.

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Contributed by: D. Meliga, A. Ratti, L. Lavagnino and S. Z. Lavagnino (August 2022)
Open content licensed under CC BY-NC-SA

Snapshots

Details

Snapshot 1: Isothermal expansion. At constant temperature, expanding the volume causes a compression in the energy-level spacing. As a consequence, more levels are occupied and the system entropy increases ).

Snapshot 2: Isochoric heating. As the energy levels remain unchanged, rising temperature causes increased occupation of higher energy levels. The system entropy thus increases ).

Snapshot 3: Adiabatic expansion. Expansion in volume causes a decreased spacing of the levels. A decrease in temperature leads to decreased occupancy of higher levels. The two effects compensate and the entropy remains constant , ).

Reference

[1] P. Atkins and L. Jones, Chemical Principles: The Quest for Insight, New York: W. H. Freeman, 1999.

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