Maximum work configurations of finite potential capacity reservoir chemical engines

Abstract

An isothermal endoreversible chemical engine operating between the finite potential capacity high-chemical-potential reservoir and the infinite potential capacity low-chemical-potential reservoir has been studied in this work. Optimal control theory was applied to determine the optimal cycle configurations corresponding to the maximum work output per cycle for the fixed total cycle time and a universal mass transfer law. Analyses of special examples showed that the optimal cycle configuration with the mass transfer law g ∝ Δµ, where Δµ is the chemical potential difference, is an isothermal endoreversible chemical engine cycle, in which the chemical potential (or the concentration) of the key component in the working substance of low-chemical-potential side is a constant, while the chemical potentials (or the concentrations) of the key component in the finite potential capacity high-chemical-potential reservoir and the corresponding side working substance change nonlinearly with time, and the difference of the chemical potentials (or the ratio of the concentrations) of the key component between the high-chemical-potential reservoir and the working substance is a constant. While the optimal cycle configuration with the mass transfer law g ∝ Δc, where Δc is the concentration difference, is different from that with the mass transfer law g ∝ Δµ significantly. When the high-chemical-potential reservoir is also an infinite potential capacity chemical potential reservoir, the optimal cycle configuration of the isothermal endoreversible chemical engine consists of two constant chemical potential branches and two instantaneous constant mass-flux branches, which is independent of the mass transfer law. The object studied in this paper is general, and the results can provide some guidelines for optimal design and operation of real chemical engines.