Unified Description of Isothermal Endoreversible Chemical Cycles with Linear Mass Transfer Law

Abstract

An isothermal endoreversible four-reservoir chemical pump cycle operating between a finite potential capacity high-chemical-potential mass reservoir and three infinite potential capacity mass reservoirs is established in this paper. Optimal control theory is applied to determine the optimal cycle configuration corresponding to the maximum energy output per cycle for the fixed total cycle time and transferred energy of high-chemical-potential mass reservoir in which the mass transfer between working fluid and mass reservoirs obey linear mass transfer law. The optimal cycle configuration is an isothermal endoreversible four-reservoir chemical pump cycle, in which the chemical potential (the concentration) of the key component in the finite potential capacity high-chemical-potential mass reservoir and that in the working fluid change nonlinearly with time and the difference between the chemical potential (the ratio of the concentration) of the key component in the finite potential capacity mass reservoir and (to) that in the working fluid is a constant, and the chemical potentials (the concentration) of the key component in the working fluid at the infinite potential capacity mass reservoir sides are also constants. Moreover, the numerical example is provided to reveal the influences of concentration and chemical potential change of the finite potential capacity high-chemical-potential mass reservoir on the optimal configuration of the four-reservoir chemical pump cycle. Then, a unified description of various isothermal endoreversible chemical cycles with linear mass transfer law is obtained. They include ten type of isothermal endoreversible chemical cycles: four-reservoir chemical pumps with finite potential capacity mass reservoirs and infinite potential capacity mass reservoirs, four-reservoir chemical potential transformers with finite potential capacity mass reservoir and infinite potential capacity mass reservoirs, three- reservoir chemical pumps with finite potential capacity mass reservoirs and infinite potential capacity mass reservoirs, three-reservoir chemical potential transformers with finite potential capacity mass reservoir and infinite potential capacity mass reservoirs, two-reservoir chemical pump with infinite potential capacity mass reservoirs, and chemical engine with infinite potential capacity mass reservoirs. The results can provide some guidelines for optimal design and operation of real chemical cycles and devices.