Efficiency at maximum power of Feynman's ratchet as a heat engine
Abstract
Description
The maximum power of Feynman's ratchet as a heat engine and the corresponding efficiency ($η_\ast$) 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 $η_\ast =η_C^2 /[η_C-(1-η_C)\ln(1-η_C)]$, where $η_C\equiv 1-T_2/T_1$. 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 $η_{SS}\equiv 2η_C/(4-η_C)$ 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 $η_\ast$ and $η_{SS}$ 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.
7 pages, 3 figures; correct some errors
7 pages, 3 figures; correct some errors