The aim of this research has been to investigate the role of the second law in thermoelectric phenomena. Considering the thermoelectric generator as a heat engine cycle process, the Kelvin relations for the thermoelectric circuit are derived from the energy balance and from the second law without using reversibility or equilibrium assumptions. A new formula has been derived for the thermal efficiency of the thermoelectric generator, also taking into account Thomson heat. An equation for maximum efficiency is derived and a representative numerical example of this equation is presented.