Performance Analysis and Optimization for Irreversible Combined Carnot Heat Engine Working with Ideal Quantum Gases

Abstract

An irreversible combined Carnot cycle model using ideal quantum gases as a working medium was studied by using finite-time thermodynamics. The combined cycle consisted of two Carnot sub-cycles in a cascade mode. Considering thermal resistance, internal irreversibility, and heat leakage losses, the power output and thermal efficiency of the irreversible combined Carnot cycle were derived by utilizing the quantum gas state equation. The temperature effect of the working medium on power output and thermal efficiency is analyzed by numerical method, the optimal relationship between power output and thermal efficiency is solved by the Euler-Lagrange equation, and the effects of different working mediums on the optimal power and thermal efficiency performance are also focused. The results show that there is a set of working medium temperatures that makes the power output of the combined cycle be maximum. When there is no heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are parabolic-like ones, and the internal irreversibility makes both power output and efficiency decrease. When there is heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are loop-shaped ones, and the heat leakage loss only affects the thermal efficiency of the combined Carnot cycle. Comparing the power output of combined heat engines with four types of working mediums, the two-stage combined Carnot cycle using ideal Fermi-Bose gas as working medium obtains the highest power output.

Relativistic quantum heat engine with the presence of minimal length

“…The discussions of the quantum heat engine are about how to get a higher efficiency engine than the classic Carnot engine efficiency and get a more efficient power output [5][6][7]. Several attempts were made, such as using a harmonic oscillator as a working substance [8][9][10], utilizing quantum entanglement [11][12][13][14][15], and modifying the thermodynamic cycle [16][17][18]. Exploration of the efficiency of quantum heat engines eventually involves minimal length, which is a topic of discussion in quantum gravity [19].…”

Spectral properties of size-invariant shape transformation

“…In quantum confined systems, the discrete energy spectra make the geometry dependence of the physical properties of materials prominent, which were negligible at macroscale [5][6][7][8][9]. Quantum size effect is perhaps the best known of the geometric effects appearing at nanoscale [10][11][12][13] and the importance of the energy quantization and a few-level systems has led to the study of quantum heat machines highlighting the essence of this effect [14][15][16][17][18][19][20][21][22].…”

Global Stability of the Curzon-Ahlborn Engine with a Working Substance That Satisfies the van der Waals Equation of State

“…Other authors have studied the stability under different operating regimes, such as the regime of maximum efficiency and maximum ecological function [ 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ]. It is important to note that the finite time thermodynamics continues to address more systems of current interest, as shown in [ 25 , 26 , 27 , 28 , 29 , 30 ].…”