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Jurnal Teori dan Aplikasi Fisika

Mesin Carnot Quantum dengan Dua Partikel Tidak Berinteraksi dan Tidak Berdekatan

Khazali Fahmi

Published Jul 24, 2023• 0 citations
Publisher

Abstract

In this article, we study the quantum Carnot engine using a one-dimensional infinite well potential model in which two particles are non-interacting, indistinguishable and have the same mass. We find that the efficiency of this model is the same as that of the one-dimensional infinite potential well model in which there is one particle. Moreover, efficiency can be measured only when L_C/L_A≥2, where L_A and L_C are the potential well widths during isothermal and adiabatic expansion, respectively.

DOI
10.23960/2fjtaf.v11i2.11060

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In this article, we study the quantum Carnot engine using a one-dimensional infinite well potential model in which two particles are non-interacting, indistinguishable and have the same mass. We find that the efficiency of this model is the same as that of the one-dimensional infinite potential well model in which there is one particle. Moreover, efficiency can be measured only when L_C/L_A≥2, where L_A and L_C are the potential well widths during isothermal and adiabatic expansion, respectively.
Telah dijabarkan proses-proses termodinamika kuantum pada siklus mesin Carnot kuantum tiga dimensi dengan substansi kerja berupa sistem dua tingkat sumur potensial takhingga dengan lebar Lx; Ly dan Lz. Hasil-hasil ditiap proses berupa tenaga dalam sistem E, gaya F yang bekerja pada sistem, kerja W sistem, dan pertukaran bahang Q selama proses hingga didapatkan formulasi total kerja sistem dalam satu kali siklus. Awalnya ditunjukkan prosesproses untuk sistem dua tingkat mesin Carnot kuantum satu dimensi berupa pengembangan-penyusutan isotermal dan pengembangan-penyusutan adiabatik kemudian diselesaikan untuk kasus tiga dimensi. Didapatkan juga efisiensi ?? dari mesin Carnot kuantum tiga dimensi yang beranalogi dengan efisiesni mesin Carnot klasik. We have evaluated each quantum thermodynamic process of three dimensional quantum Carnot engine where infinite well potential width Lx; Ly and Lz as a work substance. The results of each process are internal energy system (E), force (F) exerts the potential wall of system, work W and heat exchange Q during the process until we get a total work formulation of system in one cycles. First, will be shown the processes for two level system of one dimensional quantum Carnot engine such as expanding-compressing Isothermal and expanding-compressing adiabatic then be finished for three dimensional case. We also calculated the efficiency ?? of three dimensional quantum Carnot engine which analogizes by efficiency of classical Carnot engine.
A cyclic thermodynamic heat engine,which combines adiabatic and isothermal processes and consists of classical ideal gas as working substance,runs most efficiently if it is reversible.In this paper,A new cyclic model of quantum Carnot heat engine whose working substance consists of non-interacting extreme relativistic particles confined to an infinite potential well,is set up.It is shown that the engine whose cycle consists of adiabatic and isothermal quantum processes are close analogues of the corresponding classical processes and that the efficiency of this engine is equal to the Carnot efficiency because quantum dynamics is reversible.Consequently,the expectation value of the Hamiltonian in the expression of the efficiency is similar to the temperature in that of the classical one.
A multiple-state quantum Carnot engine based on single particle in one dimensional potential well is evaluated. The general forms of adiabatic and isothermal force as well as work are given. We apply them first to the simplest case of two-state system, and then to three-state and general n-state system. The first isothermal expansion starts from single ground state and cease to single highest state. In Addition to the simplest case, isothermal expansions may terminate not to highest state but an intermediate state but with the same of the total expansion. The result is that the efficiency of the multi-state machine could be enhanced by reducing the volume of isothermal expansion for the same of the total volume expansion.
In their work [J. Phys. A 33, 4427 (2000)], Bender, Brody, and Meister have shown by employing a two-state model of a particle confined in the one-dimensional infinite potential well that it is possible to construct a quantum-mechanical analog of the Carnot engine through changes of both the width of the well and the quantum state in a specific manner. Here, a discussion is developed about realizing the maximum power of such an engine, where the width of the well moves at low but finite speed. The efficiency of the engine at the maximum power output is found to be universal independently of any of the parameters contained in the model.
Carnot model of heat engine is the most efficient cycle consisting of isothermal and adiabatic processes which are reversible. Although ideal gas usually used as a working fluid in the Carnot engine, Bender used quantum particle confined in 1D potential well as a working fluid. In this paper, by following Bender we generalize the situation to 2D symmetric potential well. The efficiency is express as the ratio of the initial length of the system to the final length of the compressed system. The result then is shown that for the same ratio, 2D potential well is more efficient than 1D potential well.
Carnot cycle consists of isothermal and adiabatic processes which are reversible. Using analogy in quantum mechanics, these processes can be well explained by replacing variables in classical process with a quantum system. Quantum system which is shown in this paper is a particle that moves under the influence of a cubic potential which is restricted only to the state of the two energy levels. At the end, the efficiency of the system is shown as a function of the width ratio between the initial conditions and the farthest wall while expanding. Furthermore, the system efficiency will be considered 1D and 2D cases. The providing efficiencies are different due to the influence of the degeneration of energy and the degrees of freedom of the system.