The fundamental equations of thermoelectricity are reviewed in a more general and rigorous context and the efficiency quotient of the thermoelements is derived, with emphasis on the relevance of the figure of merit parameter. The Joule–Lenz, thermoelectric and thermoconducted heat are identified, and the ideal situation of a perfectly homogeneous sample subjected to small temperature and voltage gradients is discussed. Thomson heat and the related Peltier effect arising at local inhomogeneities, such as junctions, are also analyzed. In this context, the efficiency quotient is derived for an ideal thermoelectric sample, which reveals a new figure of merit parameter. It is checked explicitly that the efficiency quotient is always lower than the Carnot efficiency quotient, and it is shown that the new figure of merit never exceeds unity.