Bounds of efficiency at maximum power for linear, superlinear and sublinear irreversible Carnot-like heat engines

TL;DR

This paper analyzes the efficiency at maximum power (EMP) of various types of irreversible Carnot-like heat engines, establishing bounds based on their constitutive relations and thermodynamic assumptions.

Contribution

It classifies Carnot-like heat engines into linear, superlinear, and sublinear types and derives bounds for their EMP under weak endoreversible and irreversible thermodynamics assumptions.

Findings

EMP bounds are between η_C/2 and η_C/(2-η_C) for linear engines.

Superlinear engines have EMP bounds from 0 to η_C/(2-η_C).

Sublinear engines' EMP bounds are from η_C/2 to η_C.

Abstract

The efficiency at maximum power (EMP) of irreversible Carnot-like heat engines is investigated based on the weak endoreversible assumption and the phenomenologically irreversible thermodynamics. It is found that the weak endoreversible assumption can reduce to the conventional one for the heat engines working at maximum power. Carnot-like heat engines are classified into three types (linear, superlinear, and sublinear) according to different characteristics of constitutive relations between the heat transfer rate and the thermodynamic force. The EMPs of Carnot-like heat engines are proved to be bounded between $\eta_C/2$ and $\eta_C/(2-\eta_C)$ for the linear type, 0 and $\eta_C/(2-\eta_C)$ for the superlinear type, and $\eta_C/2$ and $\eta_C$ for the sublinear type, respectively, where $\eta_C$ is the Carnot efficiency.