Efficiency of a thermodynamic motor at maximum power

Abstract

Several recent theories address the efficiency of a macroscopic thermodynamic motor at maximum power and question the so-called "Curzon-Ahlborn (CA) efficiency." Considering the entropy exchanges and productions in an n-sources motor, we study the maximization of its power and show that the controversies are partly due to some imprecision in the maximization variables. When power is maximized with respect to the system temperatures, these temperatures are proportional to the square root of the corresponding source temperatures, which leads to the CA formula for a bi-thermal motor. On the other hand, when power is maximized with respect to the transitions durations, the Carnot efficiency of a bi-thermal motor admits the CA efficiency as a lower bound, which is attained if the duration of the adiabatic transitions can be neglected. Additionally, we compute the energetic efficiency, or "sustainable efficiency," which can be defined for n sources, and we show that it has no other universal upper bound than 1, but that in certain situations, favorable for power production, it does not exceed 1/2.

References in corpus (7)

• Efficiency at maximum power: An analytically solvable model for stochastic heat engines
• Efficiency at maximum power of low dissipation Carnot engines
• Efficiency at maximum power of Feynman's ratchet as a heat engine
• Efficiency of autonomous soft nano-machines at maximum power
• Efficiency of molecular motors at maximum power
• Efficiency at maximum power output of linear irreversible Carnot-like heat engines
• Molecular kinetic analysis of a finite-time Carnot cycle

Cited by in corpus (10)

• Phase transition in protocols minimizing work fluctuations
• Efficiency at maximum power output of an irreversible Carnot-like cycle with internally dissipative friction
• Bounds of efficiency at maximum power for linear, superlinear and sublinear irreversible Carnot-like heat engines
• Geometric Heat Engines Featuring Power that Grows with Efficiency
• Network analysis of the performance of organic photovoltaic cells: The open circuit voltage and the zero current efficiency
• Thermoelectric generator at optimal power with external and internal irreversibilities
• Near-equilibrium universality and bounds on efficiency in quasi-static regime with finite source and sink
• Efficiencies of power plants, quasi-static models and the geometric-mean temperature
• Coupled autonomous thermal machines and efficiency at maximum power
• Bounds and phase diagram of efficiency at maximum power for tight-coupling molecular motors