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The heat exchanger effect on the power input of a gas refrigerator with a given cooling load is analyzed. The finite-time thermodynamic model adopted is a Brayton cycle coupled to a heat source and a heat sink with two heat exchangers. Both the heat source and heat sink have infinite heat capacity rates. Mathematical expressions for minimum power input and other characteristics of the refrigerator at minimum power are obtained for the cycle. The results of this theoretical work provide base line criteria for use in the performance evaluation and design of such refrigeration cycles as well as for use in performance comparisons with existing refrigerators.