Numerical Experiments of a Finite-Time Thermodynamic Cycle

Abstract

Heat engines are ubiquitous in our industrial society and are also crucially important to the basis of thermodynamics. They allow us to extract useful work from the heat flowing from a hot heat reservoir into a cold heat reservoir by expanding and compressing the working substance. We have already known that the upper bound of the efficiencies of all the existing heat engines is limited by the Carnot efficiency ηC ≡ 1− Tc/Th where Th and Tc are the temperatures of the hot and the cold reservoirs, respectively. ηC can be realized only when heat engines are working infinitely slowly (quasistatic limit). This implies that the heat engine working in the quasistatic limit produces zero power because it takes infinite time to produce a finite amount of work. Though the Carnot efficiency is a fundamental result which manifests the natural law of the heat energy conversion and supplies certain guidance for designing efficient heat engines, it is not useful for describing the realistic heat engines which should produce finite power. Therefore, it is important to question: Are there any physical laws which can be applied to finite-time heat engines? Motivated by the above considerations, Curzon and Ahlborn studied the efficiency of a finite-time Carnot cycle and derived the result that the efficiency at the maximal power output ηmax becomes