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The second law of thermodynamics is used to study the performance of single-stage and two-stage ammonia–water absorption refrigeration systems (ARSs) when some input design parameters are varied. The entropy generation of each component and the total entropy generation ( S ̇ _tot ) of all the system components as well as the coefficient of performance (COP) of the ARSs are calculated from the thermodynamic properties of the working fluids at various operating conditions. The results show that the two-stage system has a higher S ̇ _tot and COP, while the single-stage system has a lower S ̇ _tot and COP. This is a paradox since one would expect that an efficient thermal system should have a higher COP and lower S ̇ _tot . This anomaly is explained with respect to the performance results for both single and two-stage systems. The trend in COP and S ̇ _tot with the change in heat exchangers …