The role of the Stefan-Boltzmann law in the thermodynamic optimization of an n-Müser engine

A Müser-type engine model can be taken as a particular case of a Curzon-Ahlborn thermal cycle, when the upper thermal conductance is finite and the lower one is infinite. In addition, the upper heat exchange is given by the Stefan-Boltzmann law. That model is suitable to thermodynamically describe some aspects of energy converters as solar cells and photosynthetic systems. In the present article, we call n-Müser engine to an engine of the Müser type in which the T4 heat transfer law is substituted by a Tn-law, being n>0 a real number. Here, we show that if we use the so-called ecological criterion of merit to optimize finite-time heat engines to compare the thermodynamic performance of the n-Müser engines under approximate terrestrial conditions (see below), we obtain that n=4 accomplishes the best performance. This same result was obtained by using data from the rest of planets of the solar system.