Maximum work configurations of finite potential capacity reservoir chemical engines

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.

[1]  Fengrui Sun,et al.  Maximum power of a•combined-cycle isothermal chemical engine , 1997 .

[2]  Thermodynamics of chemical power generators , 2008 .

[3]  F. Curzon,et al.  Efficiency of a Carnot engine at maximum power output , 1975 .

[4]  F. Sun,et al.  Fundamental optimal relation of a generalized irreversible four-reservoir chemical pump , 2008 .

[5]  Alexis De Vos,et al.  Endoreversible thermodynamics and chemical reactions , 1991 .

[6]  B. Holländer,et al.  Si+ ion implantation for strain relaxation of pseudomorphic Si1−xGex/Si(100) heterostructures , 2009 .

[7]  Lingen Chen,et al.  Optimal performance of an endoreversible chemical pump with diffusive mass transfer law , 2008 .

[8]  Lingen Chen,et al.  Optimal configuration of a two-heat-reservoir heat-engine with heat-leak and finite thermal-capacity , 2006 .

[9]  A. M. Tsirlin,et al.  Thermodynamic analysis and thermodynamic efficiency of chemical reactors. , 2006, Journal of Physical Chemistry B.

[10]  Jincan Chen,et al.  Optimization of performance characteristics in a class of irreversible chemical pumps , 2006, Math. Comput. Model..

[11]  Jincan Chen,et al.  General performance characteristics of an irreversible three source chemical pump , 2003 .

[12]  Lingen Chen,et al.  Effect of mixed heat-resistances on the optimal configuration and performance of a heat-engine cycle , 2006 .

[13]  Lingen Chen,et al.  Optimal performance of an endoreversible three-mmass-reservoir chemical potential transformer with diffusive mass transfer law , 2008 .

[14]  Fengrui Sun,et al.  Optimal paths for a light-driven engine with a linear phenomenological heat transfer law , 2010 .

[15]  Jincan Chen,et al.  Optimal performance of a generalized Carnot cycle for another linear heat transfer law , 1990 .

[16]  Yehuda B. Band,et al.  The generalized Carnot cycle: A working fluid operating in finite time between finite heat sources and sinks , 1983 .

[17]  Lingen Chen,et al.  Endoreversible four-reservoir chemical pump , 2007 .

[18]  Stanislaw Sieniutycz,et al.  Finite time generalization of thermal exergy , 1998 .

[19]  Karl Heinz Hoffmann,et al.  Thermo-mechanical systems with several heat reservoirs: maximum power processes , 2005 .

[20]  Fengrui Sun,et al.  The minimum heat consumption for heat-driven binary separation processes with linear phenomenological heat transfer law , 2009 .

[21]  Jincan Chen,et al.  Optimal analysis on the cyclic performance of a class of chemical pumps , 2001 .

[22]  A. D. Vos,et al.  Entropy fluxes, endoreversibility, and solar energy conversion , 1993 .

[23]  S. Sieniutycz,et al.  Thermodynamic Optimization of Finite-Time Processes , 2000 .

[24]  Bjarne Andresen,et al.  Maximum work from a finite reservoir by sequential Carnot cycles , 1981 .

[25]  A. D. Vos,et al.  Endoreversible thermodynamics of solar energy conversion , 1992 .

[26]  Fengrui Sun,et al.  Optimal configuration and performance for a generalized Carnot cycle assuming the heat-transfer law Q∝(ΔT)m , 2004 .

[27]  Lawrence S. Chen.  Performance characteristic of isothermal chemical engines , 1997 .

[28]  Fengrui Sun,et al.  Optimal performance of a generalized irreversible four-reservoir isothermal chemical potential transformer , 2008 .

[29]  Jeffrey M. Gordon,et al.  Maximum work from isothermal chemical engines , 1993 .

[30]  Fengrui Sun,et al.  Performance of Combined-Cycle Chemical Engines with Mass Leak , 1999 .

[31]  Fengrui Sun,et al.  Optimal configuration of a class of endoreversible heat engines for maximum efficiency with radiative heat transfer law , 2008 .

[32]  Fengrui Sun,et al.  Optimal configuration for a finite high-temperature source heat engine cycle with the complex heat transfer law , 2009 .

[33]  Jeffrey M. Gordon,et al.  Performance characteristics of endoreversible chemical engines , 1993 .

[34]  Itamar Procaccia,et al.  On the efficiency of rate processes. Power and efficiency of heat engines , 1978 .

[35]  Wang Jian-Hui,et al.  Performance of a quantum heat engine cycle working with harmonic oscillator systems , 2007 .

[36]  Bjarne Andresen,et al.  Thermodynamics for Processes in Finite Time , 1984 .

[37]  F. Sun,et al.  Optimal performance of an endoreversible chemical engine with diffusive mass transfer law , 2008 .

[38]  Fengrui Sun,et al.  The optimal path of piston motion for Otto cycle with linear phenomenological heat transfer law , 2009 .

[39]  Stanislaw Sieniutycz,et al.  Complex chemical systems with power production driven by heat and mass transfer , 2009 .

[40]  Karl Heinz Hoffmann,et al.  Maximum power processes for multi-source endoreversible heat engines , 2004 .

[41]  Jincan Chen,et al.  Irreversible chemical-engines and their optimal performance analysis , 2004 .

[42]  Stanislaw Sieniutycz,et al.  Analysis of power and entropy generation in a chemical engine , 2008 .

[43]  Lingen Chen,et al.  Performance of a four-reservoir chemical potential transformer with irreversible mass transfer and mass leakage , 2007 .

[44]  Fengrui Sun,et al.  Maximum power configuration for multireservoir chemical engines , 2009 .

[45]  Fengrui Sun,et al.  Performance of chemical engines with a mass leak , 1998 .

[46]  A. M. Tsirlin,et al.  Finite time thermodynamics: limiting performance of diffusion engines and membrane systems. , 2005, The journal of physical chemistry. A.

[47]  Lingen Chen,et al.  Finite Time Thermodynamic Optimization or Entropy Generation Minimization of Energy Systems , 1999 .

[48]  A. D. Vos.  Is a solar cell an endoreversible engine , 1991 .

[49]  Chih Wu,et al.  The equivalent combined cycle of an irreversible chemical potential transformer and its optimal performance , 2002 .

[50]  Stanislaw Sieniutycz,et al.  Nonlinear thermokinetics of maximum work in finite time , 1998 .