Not all counterclockwise thermodynamic cycles are refrigerators

Abstract

Clockwise cycles on PV diagrams always represent heat engines. It is therefore tempting to assume that counterclockwise cycles always represent refrigerators. This common assumption is incorrect: most counterclockwise cycles cannot be refrigerators. This surprising result is explored here for quasi-static ideal gas cycles, and the necessary conditions for refrigeration cycles are clarified. Three logically self-consistent criteria can be used to determine if a counterclockwise cycle is a refrigerator. The most fundamental test compares the counterclockwise cycle with a correctly determined corresponding Carnot cycle. Other criteria we employ include a widely accepted description of the functional behavior of refrigerators, and a corollary to the second law that limits a refrigerator's coefficient of performance.