2011/12/06 by M. Moreau, Bernard Gaveau, B. Gaveau +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Adiabatic process #Advanced Thermodynamics and Statistical Mechanics #Carnot cycle #Field-Flow Fractionation Techniques #Mathematical analysis #Mathematical optimization #Mathematics #Maximization #Maximum power principle #Phase Equilibria and Thermodynamics #Physics #Power (physics) #Thermodynamics #Upper and lower bounds #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.85.021129
arxiv created 2011/12/06 · openalex publication_date 2012/02/21 · arxiv updated 2015/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 bithermal motor. On the other hand, when power is maximized with respect to the transition durations, the Carnot efficiency of a bithermal 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, which are favorable for power production, it does not exceed ½.