Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

The Carnot Cycle, Reversibility and Entropy

Version 1 : Received: 31 May 2021 / Approved: 1 June 2021 / Online: 1 June 2021 (14:59:55 CEST)

A peer-reviewed article of this Preprint also exists.

Sands, D. The Carnot Cycle, Reversibility and Entropy. Entropy 2021, 23, 810. Sands, D. The Carnot Cycle, Reversibility and Entropy. Entropy 2021, 23, 810.

Journal reference: Entropy 2021, 23, 810
DOI: 10.3390/e23070810


The Carnot cycle and the attendant notions of reversibility and entropy are examined. It is shown how the modern view of these concepts still correspond to the ideas Clausius laid down in the nineteenth century. As such, they reflect the outmoded idea current at the time that heat is motion. It is shown how this view of heat led Clausius to develop the entropy of a body based on the work that could be done in a reversible process rather than the work that was actually done. In consequence, Clausius built into entropy a conflict with energy conservation, which is concerned with actual changes in energy. In this paper, a macroscopic formulation of internal mechanisms of damping based on rate equations for the distribution of energy within a gas. It is shown that work processes involving a step-change in external pressure, however small, are intrinsically irreversible. However, under idealised conditions of zero damping the gas inside a piston expands and traces out a trajectory through the space of equilibrium states. Therefore, the entropy change due to heat flow from the reservoir matches the entropy change of the equilibrium states. This trajectory can traced out in reverse as the piston reverses direction, but if the external conditions are adjusted appro-priately, the gas can be made to trace out a Carnot cycle in P-V space. The cycle is dynamic as opposed to quasi-static as the piston has kinetic energy equal in difference to the work done in-ternally and externally.


Carnot cycle; entropy; reversibility; irreversibility; Clausius



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