Near-equilibrium universality and bounds on efficiency in quasi-static regime with finite source and sink

Ramandeep S. Johal, Renuka Rai

Published 2014-12-01Version 1

We consider efficiency at maximum work extraction via quasi-static processes when the heat source and the sink can be modeled as identical thermodynamic systems at different initial temperatures T_+ and T_-, respectively. Though the efficiency, in general, depends on the fundamental relation describing these systems, we find that for small difference of temperatures, the efficiency is function only of the ratio of initial temperatures. We also model different sizes of source and sink by combining copies of the same thermodynamic system. The efficiency of this process in near-equilibrium regime is \eta = \eta_C / (2 - \gamma \eta_C), where \eta_C is the Carnot efficiency and parameter \gamma depends only on the relative size of the source and the sink. It follows that in this setup the efficiency at maximum work is bounded from below and above by (\eta_C)/2 and \eta_C / (2 - \eta_C), respectively. These bounds are the same as obtained for efficiency at maximum power in certain finite-time models of heat engines.