Generalized Kelvin Formulation of the Second Law of Thermodynamics

The Kelvin formulation of the second law of thermodynamics permits the following generalization: If the efficiency of a heat engine approaches unity, then the rejected work vanishes. This generalization allows deriving the behavior of a Carnot cycle near absolute zero of temperature. Also, the unattainability of absolute zero can be shown. In turn, these results allow deriving the behavior of the entropy near absolute zero, as has already been shown previously. The point of view is the phenomenological, macroscopic, and non-statistical one of classical thermodynamics.