Bounds of Efficiency at Maximum Power for Normal-, Sub- and Super-Dissipative Carnot-Like Heat Engines

TL;DR

This paper establishes bounds on the efficiency at maximum power for different classes of Carnot-like heat engines, based on their dissipation characteristics, providing a unified understanding of their performance limits.

Contribution

It derives universal bounds for efficiency at maximum power for normal-, sub-, and super-dissipative Carnot-like engines, extending previous results to a broader class of irreversible engines.

Findings

Efficiency bounds for normal-dissipative engines: $rac{ extit{ exteta}_C}{2}$ to $rac{ extit{ exteta}_C}{2- extit{ exteta}_C}$

Efficiency bounds for sub-dissipative engines: $rac{ extit{ exteta}_C}{2}$ to $ extit{ exteta}_C$

Efficiency bounds for super-dissipative engines: 0 to $rac{ extit{ exteta}_C}{2- extit{ exteta}_C}$

Abstract

The Carnot-like heat engines are classified into three types (normal-, sub- and super-dissipative) according to relations between the minimum irreversible entropy production in the "isothermal" processes and the time for completing those processes. The efficiencies at maximum power of normal-, sub- and super-dissipative Carnot-like heat engines are proved to be bounded between $\eta_C/2$ and $\eta_C/(2-\eta_C)$, $\eta_C /2$ and $\eta_C$, 0 and $\eta_C/(2-\eta_C)$, respectively. These bounds are also shared by linear, sub- and super-linear irreversible Carnot-like engines [Tu and Wang, Europhys. Lett. 98, 40001 (2012)] although the dissipative engines and the irreversible ones are inequivalent to each other.