Efficiency of a Curzon and Ahlborn engine with Dulong-Petit heat transfer law

Abstract

Using the maximization of the power output per cycle, the optimization of a thermal engine performing a Carnot-type cycle is considered. It is assumed that the heat transfer between the reservoirs and the engine occurs according to the Dulong and Petit's heat transfer law. It is found that the efficiency obtained with this heat transfer law can be written as a power series in the parameter $\lambda\sim 1/(\ln{V_{max}}-\ln{V_{min}})$, where $V_{max}$ and $V_{min}$ are the maximum volume and minimum volume spanned by the cycle, respectively. It is also shown that the calculated efficiency verifies the semi-sum property of the ecological efficiency.