Efficiency at maximum power of a chemical engine

Abstract

A cyclically operating chemical engine is considered that converts chemical energy into mechanical work. The working fluid is a gas of finite-sized spherical particles interacting through elastic hard collisions. For a generic transport law for particle uptake and release, the efficiency at maximum power νmp takes the form 1/2 + c μ + O( μ2), with 1/2 a universal constant and μ the chemical potential difference between the particle reservoirs. The linear coefficient c is zero for engines featuring a so-called left/right symmetry or particle fluxes that are antisymmetric in the applied chemical potential difference. Remarkably, the leading constant in νmp is non-universal with respect to an exceptional modification of the transport law. For a nonlinear transport model, we obtain νmp, with θ > 0 the power of μ in the transport equation.