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

Abstract

The maximum power of Feynman's ratchet as a heat engine and the corresponding efficiency (η*) 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 pawl via kinetic energy) works between two thermal baths at temperatures T1 > T2, its efficiency at maximum power is found to be η* = η2C/[ηC - (1 - ηC)ln(1 - ηC)], where ηC ≡ 1 - T2/T1. This efficiency is slightly higher than the value obtained by Curzon and Ahlborn (1975 Am. J. Phys. 43 22) for macroscopic heat engines. It is also slightly larger than the result ηSS ≡ 2ηC/(4 - ηC) obtained by Schmiedl and Seifert (2008 EPL 81 20003) for stochastic heat engines working at small temperature differences, while the evident deviation between η* and ηSS appears at large temperature differences. For an imperfect ratchet device in which the heat exchange between the ratchet and the pawl via kinetic energy is non-vanishing, the efficiency at maximum power decreases with increase in the heat conductivity. © 2008 IOP Publishing Ltd.