Abstract
In this paper, we analyze the total work extracted and the efficiency of the magnetic Otto cycle in its classic and quantum versions. As a general result, we found that the work and efficiency of the classical engine is always greater than or equal to its quantum counterpart, independent of the working substance. In the classical case, this is due to the fact that the working substance is always in thermodynamic equilibrium at each point of the cycle, maximizing the energy extracted in the adiabatic paths. We apply this analysis to the case of a two-level system, finding that the work and efficiency in both the Otto’s quantum and classical cycles are identical, regardless of the working substance, and we obtain similar results for a multilevel system where a linear relationship between the spectrum of energies of the working substance and the external magnetic field is fulfilled. Finally, we show an example of a three-level system in which we compare two zones in the entropy diagram as a function of temperature and magnetic field to find which is the most efficient region when performing a thermodynamic cycle. This work provides a practical way to look for temperature and magnetic field zones in the entropy diagram that can maximize the power extracted from an Otto magnetic engine.
Highlights
The classical standard nonmagnetic Otto cycle is widely used in present-day technology, as it is the thermodynamic cycle most commonly found in automobiles engines
In this work we have studied and compared Otto’s classical and quantum cycles, showing that the amount of extracted work under classical formulation is equal to or higher than its quantum counterpart
An explanation for this lies in all-timing equilibrium configurations along the cycle operation in the classical one, while in the quantum case, the only equilibrium states belong to the thermal reservoirs
Summary
The classical standard nonmagnetic Otto cycle is widely used in present-day technology, as it is the thermodynamic cycle most commonly found in automobiles engines. The system interacts with either of two thermal reservoirs at temperatures Tl and Th , with Th > Tl , and each one of these processes is followed by a classical adiabatic process which enables work extraction In this cycle, the results of the efficiency depend on the nature of the working substance (through its energy spectrum) and the contributions of work and heat are separate in its stages, which facilitates theoretical modelling. The quantum scenario requires that the energy-level populations of the working substance remain constant for each of the quantum states as the volume varies, ensuring that entropy remains unchanged This implies that the quantum adiabatic processes should be realized in a time frame that avoids transitions between levels that can be generated while it is carried out. We explore the consequences of including more energy levels and how this affects the behavior of thermal quantities and work as compared to the simple case of a two-level system
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