Effects of mass transfer laws on finite time exergy

摘要

The problem of the maximal work that can be extracted from a system consisting of one infinite chemical potential reservoir and one subsystem is investigated in this paper. Finite time exergy is derived for the fixed duration of the process by applying optimal control theory. Effects of mass transfer laws on the finite time exergy and the corresponding optimal mass transfer processes are analysed. The optimal thermodynamic processes for the finite time exergy include two categories: one is that the chemical potential of the subsystem is a constant and the chemical potential difference between the reservoir and the subsystem is also a constant during the mass transfer process, and the other is that the chemical potential of the subsystem switches between two optimal values during the mass transfer process. Mass transfer laws have significant effects on the optimal thermodynamic process for the finite time exergy, and the necessary and sufficient condition to determine the optimal thermodynamic process is also given. The results show that the optimal thermodynamic processes with mass transfer laws [g∝Δ(μ)] and [g∝Δ(c)], where Δμ is the chemical potential difference and Ac is the concentration difference, belong to the first category, while the optimal thermodynamic processes with mass transfer laws g∝[(Δμ) + (Δμ)~n, where n is an odd number and equal to or larger than 9, belong to the second category. The finite time exergy tends to the classical thermodynamic exergy when the duration tends to infinite long. The finite time exergy is a more realistic, stronger limit compared to the classical thermodynamic exergy.