Efficiency at maximum power of Feynman's ratchet as a heat engine

TL;DR

This paper analyzes the maximum power and efficiency of Feynman's ratchet as a heat engine, deriving a new efficiency formula that slightly exceeds previous models, especially at large temperature differences.

Contribution

It provides a novel efficiency expression for Feynman's ratchet at maximum power, considering both perfect and imperfect heat exchange scenarios, extending prior theoretical models.

Findings

Efficiency at maximum power is slightly higher than Curzon-Ahlborn and Schmiedl-Seifert results.

Efficiency depends on the heat exchange between ratchet and paw, decreasing with increased heat conductivity.

Derived efficiency formula applies to ideal and non-ideal ratchet heat engines.

Abstract

The maximum power of Feynman's ratchet as a heat engine and the corresponding efficiency ($\eta_\ast$) are investigated by optimizing both the internal parameter and the external load. When a perfect ratchet device (no heat exchange between the ratchet and the paw via kinetic energy) works between two thermal baths at temperatures $T_1> T_2$, its efficiency at maximum power is found to be $\eta_\ast =\eta_C^2 /[\eta_C-(1-\eta_C)\ln(1-\eta_C)]$, where $\eta_C\equiv 1-T_2/T_1$. This efficiency is slightly higher than the value $1-\sqrt{T_2/T_1}$ obtained by Curzon and Ahlborn [\textit{Am. J. Phys.} \textbf{43} (1975) 22] for macroscopic heat engines. It is also slightly larger than the result $\eta_{SS}\equiv 2\eta_C/(4-\eta_C)$ obtained by Schmiedl and Seifert [\textit{EPL} \textbf{81} (2008) 20003] for stochastic heat engines working at small temperature difference, while the evident deviation between $\eta_\ast$ and $\eta_{SS}$ appears at large temperature difference. For an imperfect ratchet device in which the heat exchange between the ratchet and the paw via kinetic energy is non-vanishing, the efficiency at maximum power decreases with increasing the heat conductivity.