HEAT ENGINES IN FINITE-TIME GOVERNED BY MASTER-EQUATIONS

A simple example of a four-stroke engine operated in finite-time is an alyzed. The working medium consists of noninteracting two-level system s or harmonic oscillators. The cycle of operation is analogous to a fo ur-stroke Otto cycle. The only source of irreversibility is due to the finite rate of heat transfer between the working medium and the cold and hot baths. The dynamics of the working medium is governed by a mas ter equation. The engine is shown to settle to a stable limit cycle fo r given contact periods with the hot and cold baths. The operation of the engine is analyzed subject to a fixed cycle time. The time allocat ion between the hot and cold branches that maximizes the work output i s considered. Analytical results are obtained when the relaxation is v ery slow, very fast, or when the relaxation rates along the hot and co ld branches are equal. Numerical results are presented for the general case. A maximization of the power with respect to the cycle time lead s to finite optimal cycling frequency provided the adiabatic branches are allotted finite durations. (C) 1996 American Association of Physic s Teachers.