Optimal performance of an endoreversible three-mass-reservoir chemical pump with diffusive mass transfer law
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ure, the parameters µH, µL and µO are, respectively, the chemical potentials of the three reservoirs and they supposed to be constant and obey the relation: µHLO. The parameters µ1, µ2 and µ3 are, respectively, the chemical potentials of the chemicals involved in the three processes in the cycle’s working medium. Because of the existence of finite-rate mass transfer, µ1, µ2 and µ3 are, respectively, different from those of the three mass-reservoirs. The parameters ΔN1, ΔN2 and ΔN3 are, respectively, the amounts of mass exchange between the cyclic working medium and the three mass-reservoirs at chemical potentials µH, µL and µO per cycle. The parameters h1, h2 and h3 are, respectively, the mass-transfer coefficients. The parameters t1, t2 and t3 are the corresponding times spent undergoing the three mass transfer processes, and the cycle period is:
ζ=t1+t2+t3                                                                                       (1)
It is assumed that the mass exchange obeys the diffusive mass transfer law of nonlinear irreversible thermodynamics, i.e.
ΔN1=h1(exp(µH)/kT - exp(µ1)/kT)t1, ΔN2=h2(exp(µ2)/kT - exp(µL)/kT)t2, ΔN3=h3(exp(µo)/kT - exp(µ3)/kT)t3        (2)
Where k is Boltzmann’s constant and T is temperature.
Optimal performance of an endoreversible three-mass-reservoir chemical pump with diffusive mass transfer law
3. Fundamental optimal relation
According to the laws of mass and energy conservations, one has
ΔΔN1-ΔN2+ ΔN3=0                                                          (3)
µ1ΔΔN12ΔN23ΔN3=0