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Jurnal Penelitian Fisika dan Aplikasinya (JPFA)

Quantum Relativistic Diesel Engine with Single Massless Fermion in 1 Dimensional Box System

Deny Pra Setyo, Eny Latifah, Arif Hidayat, Hari Wisodo

Published Jun 30, 2018• 11 citations
Publisher

Abstract

The quantum Diesel of a single fermion in 1D box system has been explored. The Fermion particle meets the Dirac's relativistic Hamiltonian with a chosen mass worth zero. This Relativistic Diesel engine research aims to obtain Diesel engine efficiency that utilizes massless fermion particles as a working substance. This study implements a modified analogy model of the classical analogue model to quantum with the implementation of the first law of thermodynamics for quantum systems so that quantum thermodynamic processes can be defined explicitly. The exploratory results of a single quantum fermion Diesel engine of a single massless system are efficiency formulation that is suitable for the efficiency of a classic Diesel engine, but its heat capacity ratio is unique, that is 2. Based on the value of heat capacity ratio, the efficiency is higher than the classical.

DOI
10.26740/jpfa.v8n1.p25-32

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The quantum Diesel of a single fermion in 1D box system has been explored. The Fermion particle meets the Dirac's relativistic Hamiltonian with a chosen mass worth zero. This Relativistic Diesel engine research aims to obtain Diesel engine efficiency that utilizes massless fermion particles as a working substance. This study implements a modified analogy model of the classical analogue model to quantum with the implementation of the first law of thermodynamics for quantum systems so that quantum thermodynamic processes can be defined explicitly. The exploratory results of a single quantum fermion Diesel engine of a single massless system are efficiency formulation that is suitable for the efficiency of a classic Diesel engine, but its heat capacity ratio is unique, that is 2. Based on the value of heat capacity ratio, the efficiency is higher than the classical.
In this work, a quantum Otto engine (QOE) based on a multiple-state single fermion particle trapped in an one-dimensional potential well has been studied. In this study, we used an analogical model completed with the first law of thermodynamics for the quantum system. The system satisfied the relativistic Hamiltonian, especially Dirac Hamiltonian. The engine consisted of the quantum isochoric and isentropic processes to form an Otto Cycle. The heat input and output were transferred under isochoric processes. As a result, the higher the number of energies was arranged, the lower the efficiency the system has. However, we could increase the efficiency of QOE by controlling the compression ratio. In addition, we also obtained the correspondence of the efficiency ultra-relativistic limits QOE and non-relativistic limits one.
A quantum Brayton engine using a massless Boson trapped in a one-dimensional potential well as a working substance has been constructed to be studied. We used a modified analogical model by the first law of thermodynamics for a quantum system implementation. The system was built with Klein Gordon equation, relativistic quantum mechanics Hamiltonian, without the mass term of the Hamiltonian and it was trapped in a one-dimensional potential well. Then, it underwent the quantum ideal Brayton cycle process. The quantum Brayton process consisted of adiabatic compression, isobaric expansion, adiabatic expansion, and isobaric compression processes. This relativistic quantum mechanics Brayton engine has found that the efficiency formulation was similar to the classical one. This study obtained the conformity results between the quantum relativistic and classical Brayton engines. By this cycle process, we also invented that the ratio of heat capacity under constant pressure and volume of the system was 2. It could indicate that the efficiency of quantum relativistic Brayton engine is higher than the classical one.
We evaluate quantum Otto, Diesel and Brayton cycles employing multiple-state 1D box system instead of ideal gas filled cylinder. The work and heat are extracted using the change in the expectation of Hamiltonian of the system which leads to the first law of thermodynamics to quantum system. The first law makes available to redefine the force which is in fact not well defined in a quantum mechanical system and then it is applied to define the quantum version of thermodynamic processes, i.e. isobaric, isovolume and adiabatic. As the results, the efficiency of quantum Otto engine depends only on the compression ratio and will be higher than the efficiency of quantum Diesel which can decrease by the widening of expansion under isobaric process. The efficiency of quantum Brayton engine may reach maximum on certain combination between the wide of box under isobaric expansion and compression, under certain conditions. The amount of levels participated in the quantum heat engine system will potentially reduce the performance of the quantum heat cycles consisting isobaric process, but it can be resisted using isobaric process controller.
Quantum Brayton engine efficiency with the massless boson particle as a working substance has been investigated. The research method used is analogy modeling of the first law of classical thermodynamics which is implemented into the quantum systems. The quantum system used is the single massless boson particle trapped inside the two-dimensional symmetrical potential well as a replacement for the classic system is an ideal gas in a piston tube. By replacing the working substance from the classical system into a quantum system, the four processes that form the classic Brayton cycle (two isobaric processes and two adiabatic processes) can be constructed on the quantum system. The final result indicates that the quantum Brayton engine with boson particle has a higher efficiency value compared to the classic version, but is lower than that engine when the massless boson is replaced with nonrelativistic particles. This occurs because of differences in Laplace's constant value in the three systems.
A quantum dual-engine is a machine that applies a dual cycle in a quantum system. This machine is a quantum analogy to the classical dual-engine consisting of a combination of classical Otto engine and classical Diesel engine. By analogizing a particle in a one-dimensional infinite potential well as a gas in a piston-cylinder, quantum thermodynamic processes in a dual cycle can be explained from the analogies of classical processes such as adiabatic, isochoric, and isobar. This research examines the value of thermal efficiency and other aspects of the quantum dual-engine with the study of literature. The results of the research show that the thermal efficiency of the quantum dual-engine has similarities with the classical dual-engine. Under the same mechanical ratios condition, the thermal efficiency of a quantum dual-engine has a higher value than the thermal efficiency of its classical engines.
Established heat engines in quantum regime can be modeled with various quantum systems as working substances. For example, in the non-relativistic case, we can model the heat engine using infinite potential well as a working substance to evaluate the efficiency and work done of the engine. Here, we propose quantum heat engine with a relativistic particle confined in the one-dimensional potential well as working substance. The cycle comprises of two isothermal processes and two potential well processes of equal width, which forms the quantum counterpart of the known isochoric process in classical nature. For a concrete interpretation about the relation between the quantum observables with the physically measurable parameters (like the efficiency and work done), we develop a link between the thermodynamic variables and the uncertainty relation. We have used this model to explore the work extraction and the efficiency of the heat engine for a relativistic case from the standpoint of uncertainty relation, where the incompatible observables are the position and the momentum operators. We are able to determine the bounds (the upper and the lower bounds) of the efficiency of the heat engine through the thermal uncertainty relation.