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This work shows the power of the variational approach for studying the efficiency of thermal engines in the context of the Finite Time Thermodynamics (FTT). Using an endoreversible Curzon&#8211;Ahlborn (CA) heat engine as a model for actual thermal engines, three different criteria for thermal efficiency were analyzed: maximum power output, ecological function, and maximum power density. By means of this procedure, the performance of the CA heat engine with a nonlinear heat transfer law (the Stefan&#8211;Boltzmann law) was studied to describe the heat exchanges between the working substance and its thermal reservoirs. The specific case of the M&#252;ser engine for all the criteria was analyzed. The results confirmed some previous findings using other procedures and additionally new results for the M&#252;ser engine performance were obtained

A Finite-Time Thermal Cycle Variational Optimization with a Stefan–Boltzmann Law for Three Different Criteria