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Carnot cycle for an oscillator

Jacques Arnaud1, Laurent Chusseau2 and Fabrice Philippe3,4

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In 1824 Carnot established that the efficiency of cyclic engines operating between a hot bath at absolute temperature Thot and a bath at a lower temperature Tcold cannot exceed 1 − Tcold/Thot. We show that linear oscillators alternately in contact with hot and cold baths obey this principle in the quantum as well as classical regime. The expression of the work performed is derived from a simple prescription. Reversible and non-reversible cycles are illustrated. The paper begins with historical considerations and is essentially self-contained.


PACS

07.20.Pe Heat engines; heat pumps; heat pipes

05.70.Ln Nonequilibrium and irreversible thermodynamics

05.70.Ce Thermodynamic functions and equations of state

Subjects

Instrumentation and measurement

Statistical physics and nonlinear systems

Dates

Issue 5 (September 2002)

Received 21 May 2001, in final form 15 January 2002

Published 5 August 2002



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