Optimal performance of irreversible quantum Stirling refrigerator with extreme relativistic particles as working substance

In the context of finite-time thermodynamics (FTT), an irreversible quantum Stirling refrigerator (IQSR) model is constructed using extreme relativistic particles (ERP) confined within a one-dimensional infinite potential well (ODIPW) as the working medium. The cycle model is made up of two isothermal processes and two equal-L processes, where L is the width of the potential well, and the equal-L processes are treated as quantum isocapacitive processes. The occupation probability of the particles in an energy level follows the Gibbs distribution. Analytical formulas of coefficient of performance (COP, ε), cooling load (R) and Ω function are calculated. The curve of ε versus R rate is loop-shaped. The optimal performance interval, determined by cooling load and COP, can be divided into two distinct parts. One part is the optimization interval determined by the Ω function and COP optimization criteria. This interval takes the higher ε into accountwhen considering the cooling load. For instance, the maximum ε = 0.6743 is obtained when xmcop = 1.0371. The other part is the optimization interval determined by the optimization criteria of the Ω function and cooling load, which takes the higher R into account. The maximum R corresponds to R*max = 0.2918 and xmR = 1.1333. The analyses reveal that the Ω function plays a critical role in this optimization process by capturing the trade-off between COP and cooling load. The Ω function is designed to quantify the efficiency loss due to finite-time effects, thus providing a useful tool to optimize cycles in practical applications. For the quantum Stirling refrigerator, the maximum value of the Ω function (Ωmax = 0.2802) occurs when xmΩ = 1.1013 and R*mΩ = 0.2889.