Thermodynamic bounds and general properties of optimal efficiency and power in linear responses

Abstract

We study the optimal exergy efficiency and power for thermodynamic systems with Onsager-type "current-force" relationship describing the linear-response to external influences. We derive, in analytic forms, the maximum efficiency and optimal efficiency for maximum power for a thermodynamic machine described by a N × N symmetric Onsager matrix with arbitrary N . The figure of merit is expressed in terms of the largest eigenvalue of the "coupling matrix" which is solely determined by the Onsager matrix. Some simple but general relationships between the power and efficiency at the conditions for (i) maximum efficiency and (ii) optimal efficiency for maximum power are obtained. We show how the second law of thermodynamics bounds the optimal efficiency and the Onsager matrix, and relate those bounds together. The maximum power theorem (Jacobi's Law) is generalized to all thermodynamic machines with symmetric Onsager matrix in the linear-response regime. We also discuss systems with asymmetric Onsager matrix (such as systems under magnetic field) for a particular situation and we show that the reversible limit of efficiency can be reached at finite output power. Cooperative effects are found to improve the figure of merit significantly in systems with multiply cross-correlated responses. Application to example systems demonstrates that the theory is helpful in guiding the search for high performance materials and structures in energy researches.

Power-Efficiency-Dissipation Relations in Linear Thermodynamics

“…Eq. (1), splits into two separate relations, in agreement with the special cases discussed in [23,36]:…”

“…More generally, one may wonder whether there exist specific relationships between the regimes of maximum power (which will be denoted by a subscript M P ), maximum efficiency (subscript M E) and minimum dissipation (subscript mD). Recently, such relations have been discovered between M P and M E in the context of two case studies [23,36]. In this letter, we derive general relations between the three regimes, within the framework of linear irreversible thermodynamics.…”

Geometric Heat Engines Featuring Power that Grows with Efficiency

“…Heat engines that attain their maximal power and maximal efficiency (which is either the Carnot efficiency or a lower value) at different working conditions are here defined as heat engines with a power-efficiency trade-off. The power-efficiency trade-off is the subject of many recent studies [3,[6][7][8][9][10][11].Less is known about the efficiency and power of cyclic heat engines, but a lot of research effort has been devoted to understanding them in recent years [12][13][14][15][16][17][18][19]. The operation of a cyclic engine is characterized by a protocol that describes the time dependence of key variables along the cycle -e.g.…”

“…Heat engines that attain their maximal power and maximal efficiency (which is either the Carnot efficiency or a lower value) at different working conditions are here defined as heat engines with a power-efficiency trade-off. The power-efficiency trade-off is the subject of many recent studies [3,[6][7][8][9][10][11].…”

General relations between the power, efficiency, and dissipation for the irreversible heat engines in the nonlinear response regime

“…In recent years, * iyyap.si@gmail.com † ponphy@cutn.ac.in many authors were attempted to investigate the attainability of a Carnot efficiency with finite power output [42][43][44][45][46][47][48], in particular, the heat engines with broken timereversal symmetry were shown to enhance the efficiency at maximum power [42,[49][50][51][52][53][54][55]. Also the general relations between the maximum power (P MP ), the efficiency at maximum power (η MP ), the maximum efficiency (η ME ) and power at maximum efficiency (P ME ) were identified for the specific models of heat engines [56,57]. Recently, Proesmans et al obtained such a general relations for the linear irreversible heat engine with and without time-reversal symmetry (anti-symmetry) [58].…”