Alladi Ramakrishnan Hall

Duality between heat engines and refrigerators

Ramandeep S. Johal

IISER--Mohali

Heat engines and refrigerators—the two basic machines for interconversion
between heat and work, can be modelled by heat cycles operating between
two baths at different temperatures. The ideal cycle, in the forward and
reverse direction, can be regarded as replica or dual of each other—only
the direction of energy transfer is reversed on switching from the engine
to refrigerator mode. However, it is not apparent how to establish
equivalence between an irreversible engine and refrigerator. Part of the
difficulty is in the choice of analogous criteria with which to optimize
the performance of irreversible machines. In this talk, we will extend the
notion of duality to irreversible Carnot-like four-step cycles, where the
relative amounts of entropy changes/entropy generation during the cycle
are specified. The present approach is motivated by the notion of
partitioning a " whole " into parts, and is not dependent on specific form
of entropy generating terms. Our approach presents duality within both
reversible and irreversible scenarios in a unified picture. The model, at
its optimal coefficient of performance, suggests an operational principle
for the design of more efficient machines. The observations are applicable
to both finite-time as well as quasi-static cycles.