Efficiency bounds for powerful engines

Thermodynamics teaches that the efficiency of a heat engine operating between a hot reservoir at temperature T _h and a cold one at T _c can be no greater than the Carnot value η _c =1 − T _c/T _h. To achieve its theoretical maximum, the engine must run infinitely slowly and generate zero power—surely an unsatisfactory state of affairs in the real world. Now Massimiliano Esposito (Free University of Brussels) and colleagues have derived efficiency bounds for engines operating at maximum power. They assume that the engine operates in a Carnot cycle and interacts with the hot reservoir for a finite time τ_h, presumed much greater than the duration of the adiabatic steps. They then express entropy as a sum of the standard term of heat over temperature and a term of the form a _h/τ_h for some constant a _h (the...