UNIVERSALITY OF EFFICIENCY AT MAXIMUM POWER

Abstract

In this project work universality of efficiency at maximum power, maximum power and period at maximum power of finite-time thermodynamic quantities was explored. Some model heat engines were taken and universal type efficiency, especially on the first and second Taylor expansion of their analytic expressions were explored; they were found to be universal. On the other higher order terms, slight shifts have been seen. We study the efficiency at maximum power, 𝜂∗, of engines performing finite-time Carnot cycles between a hot and a cold reservoir at temperatures 𝑇ℎ and 𝑇𝑐, respectively. For engines reaching Carnot efficiency 𝜂𝑐 = 1 − 𝑇𝑐 𝑇ℎ in the reversible limit (long cycle time, zero dissipation), we find in the limit of low dissipation that, 𝜂∗, is bounded from above by 𝜂𝑐 2−𝜂𝑐 and from below by 𝜂𝑐 2 . These bounds are reached when the ratio of the dissipation during the cold and hot isothermal phases tend respectively to zero or infinity. For symmetric dissipation (ratio one) the Curzon-Ahlborn efficiency is given by 𝜂𝐶𝐴 = 1 − √𝑇𝑇𝑐ℎ is recovered.