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Second-law of thermodynamics (2nd law) and exergy analyses and optimization offour Reverse Brayton Refrigeration (RBR) cryogenic cycle configurations: Conventional 1-stage compression cycle; Conventional 2-stage compression cycle; 1-stage compressionModified cycle with intermediate cooling of the recuperator using an auxiliary cooler; andan Integrated 2-stage expansion RBR cycle are performed. The conventional RBR cyclesare analyzed for low and high pressure ratio applications using multistage compressorswith intercooling. Analytical solutions for the conventional cycles are developed includingthermal and fluid flow irreversibilities of the recuperators and all heat exchangers inaddition to the compression and expansion processes. Analytical solutions are used to findthe thermodynamic bounds for the performance of the cycles. Exergy irreversibilitydiagrams of the cycles are developed and the effects of important system parameters onRBR cycle performance are investigated. 2nd law/exergy analyses, and optimization of thecycles with intermediate cooling of the recuperator, considering the cooling temperatureand the recuperator effectiveness and pressure drop, are included. The effect of the 2ndlaw/exergy efficiency of the auxiliary cooler on the total system efficiencies is presented. [ABSTRACT FROM AUTHOR]