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When optimizing thermoelectric device design for a given set of materials and technology, the system of equations used will be different for various device applications. Whenever efficiency or coefficient of performance is important in the application, an irreversible thermodynamic analysis of the design problem is useful. In this analysis, the effects of the thermal and electrical circuit on entropy production within the device are considered. The design problem is analyzed by comparing the relative contribution of various parts of the system to the total entropy production. This irreversible thermodynamic approach is illustrated with examples concerning several different design questions. Often qualitative conclusions can be drawn more readily than with other methods.