Abstract. We study the performance of a three-terminal thermoelectric device such as heat engine and refrigerator with broken time-reversal symmetry by applying the unified trade-off figure of merit (Ω criterion) which accounts for both useful energy and losses. For heat engine, we find that a thermoelectric device working under the maximumΩ criterion gives a significantly better performance than a device working at maximum power output. Within the framework of linear irreversible thermodynamics such a direct comparison is not possible for refrigerators, however, our study indicates that, for refrigerator, the maximum cooling load gives a better performance than the maximumΩ criterion for a larger asymmetry. Our results can be useful to choose a suitable optimization criterion for operating a real thermoelectric device with broken time-reversal symmetry.
We derive the general relations between the maximum power, maximum efficiency and minimum dissipation for the irreversible heat engine in nonlinear response regime. In this context, we use the minimally nonlinear irreversible model and obtain the lower and upper bounds of the above relations for the asymmetric dissipation limits. These relations can be simplified further when the system possesses the time-reversal symmetry or anti-symmetry. We find that our results are the generalization of various such relations obtained earlier for different heat engines.
We propose a two-stage cycle for an optimized linear-irreversible heat engine that operates, in a finite time, between a hot (cold) reservoir and a finite auxiliary system acting as a sink (source) in the first (second) stage. Under the tight-coupling condition, the engine shows the low-dissipation behavior in each stage, i.e. the entropy generated depends inversely on the duration of the process. The phenomenological dissipation constants are determined within the theory itself in terms of the heat transfer coefficients and the heat capacity of the auxiliary system. We study the efficiency at maximum power and highlight a class of efficiencies in the symmetric case that show universality upto second order in Carnot efficiency, while Curzon-Ahlborn efficiency is obtained as the lower bound for this class.
A trade of figure of merit () criterion accounts the best compromise between the useful input energy and the lost input energy of the heat devices. When the heat engine is working at maximum criterion its efficiency increases significantly from the efficiency at maximum power. We derive the general relations between the power, efficiency at maximum criterion and minimum dissipation for the linear irreversible heat engine. The efficiency at maximum criterion has the lower bound and it can reach up to , where is the maximum efficiency. Further, for time-reversal symmetric or anti-symmetric case our results show that the efficiency at maximum criterion is bounded by 3/4 of the Carnot efficiency when the minimum dissipation is zero.
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