Proposal of ecologic taxes based on thermo-economic performance of a non endoreversible heat engine model

In 1995, Alexis De Vos made a thermoeconomic analysis of a model of power plant of the Novikov type in terms of the maximization of an objective function defined as the quotient of power output and the total costs of the plant operation. He analyzed this endoreversible power plant with respect to economical exploitation, and he took the optimal exploitation point lying somewhere between the maximum-power point (Curzon-Ahlborn efficiency) and the maximum-efficiency point (Carnot efficiency), with an optimum efficiency between the maximun-power efficiency and Carnot efficiency. Recently, Barranco-Jiménez and Angulo-Brown also studied a Novikov engine following the thermoeconomical approach used by De Vos, but by means of the so-called modified ecological optimization criterion. This criterion also leads to an optimal efficiency between the maximun-power efficiency and Carnot efficiency and drastically reduces the entropy production of the engine. In this work, we analyze a non endoreversible simplified thermal power plant model (the so-called Novikov engine) under economical criteria by means of the concepts of profit function and the costs involved in the performance of the power plant. In our study, two different heat transfer laws are used: the so called Newton's law of cooling and the Dulong-Petit's law of cooling. We use two finite time thermodynamic optimization criteria: the maximum power regime and the so-named modified ecological criterion for the performance analysis. This last criterion leads the engine model towards a mode of performance that appreciably diminishes the engine's wasted energy. In this work, we show that the watt price produced under maximum power conditions is lower than that produced under maximum ecological conditions. This was accomplished by using a typical definition of profits function stemming from economics. The maximum power output regime produces considerably more wasted energy towards the environment, thus the watt price under maximum power output is subsidized by nature. Due to this fact, we propose an ecological tax, which could be a certain function which is proportional to the difference between the ratio of prices of both the energy input and energy output under both the maximum power and maximum ecological regimes.