Thermodynamics in finite time. I. The step-Carnot cycle

Bjarne Andresen*, R. Stephen Berry, Abraham Nitzan, Peter Salamon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The object of this paper is the beginning of a formulation of a method to find bounds to process functions, such as work and heat, for processes occurring in finite time. A general variational statement of the problem is given. Then model problems are solved, all but one of which are based on the "step-Carnot" cycle. This is similar to the reversible Carnot cycle but with the external pressure varying in finite steps. Such a system only needs to go through a finite number of equilibrium states during its cycle. The problems are the maximization of effectiveness of the step-Carnot cycle, the maximization of efficiency of the same cycle, the determination of optimal period for a step-Carnot cycle whose contact with the external reservoirs has finite heat conductance, and the determination of the maximum power and the rate at which maximum power is obtained, for a continuous Carnot cycle with finite heat conductance between system and thermostats.

Original languageEnglish
Pages (from-to)2086-2093
Number of pages8
JournalPhysical Review A
Issue number5
StatePublished - 1977


FundersFunder number
Danish Science Foundation


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