Efficiency bounds for powerful engines
DOI: 10.1063/1.4797263
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 τh, 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/τh for some constant a h (the cold reservoir is treated analogously); placing the interaction time in the denominator ensures that the reversible-process result is obtained in the infinite-interaction-time limit. After deriving the maximum power as a function of the interaction times, Esposito and company can readily calculate the efficiency, which depends in particular on a c/a h. The figure shows the allowed range of efficiencies at maximum power. The upper bound corresponds to a c/a h = 0; the lower bound to an infinite ratio. The points in the figure give observed efficiencies for several heat engines worldwide. Those engines may not satisfy the assumptions of the Esposito model or even run in Carnot cycles; still, their efficiencies lie within or near the idealized bounds. (M. Esposito et al., Phys. Rev. Lett. 105, 150603, 2010 http://dx.doi.org/10.1103/PhysRevLett.105.150603 .)
