On Heat Engines Having Efficiencies That Degrade With Every Cycle That Are Nonetheless Reversible: The Wonders of Hilbert Curves in the Pressure-Volume Plane

Authors

Daniel GrahamFollow

Document Type

Learning Resource

Publication Date

Fall 11-7-2025

Pages

1-41

Abstract

Heat engines are cornerstones in classical thermodynamics, not to mention fixtures of everyday life. As everyone knows, real heat engines are rife with sources of irreversibility, and, in turn, have efficiencies that degrade over time. Here we chart a classical heat engine whose efficiency degrades with every cycle, but maintains perfect reversibility nonetheless. There are no paradoxes in play due to the inviolability of the thermodynamic laws. Rather the engine operates transparently according to Hilbert curves that fill the pressure-volume plane. The assembly of the curves is iterative and digital whereby no information is lost over every cycle.

Comments

Author Posting © The Author(s), 2025.

Recommended Citation

Graham, Daniel. On Heat Engines Having Efficiencies That Degrade With Every Cycle That Are Nonetheless Reversible: The Wonders of Hilbert Curves in the Pressure-Volume Plane. , , : 1-41, 2025. Retrieved from Loyola eCommons, Chemistry: Faculty Publications and Other Works,

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Copyright Statement

© The Author(s), 2025.