The order of the metals in respect of the Peltier effect was found to be the same as the thermoelectric series.
But on account of the difficulty of the measurements involved, the verification of the accurate relation between the Peltier effect and thermoelectric power was left to more recent times.
Clausius (1853) that the Peltier effect varied directly as the absolute temperature, and that the E.M.F.
(2) If the Peltier effect was proportional to the thermoelectric power and changed sign with it, as all experiments appeared to indicate, there would A B be no absorption of heat C in the circuit due to the Peltier effect, and therefore no thermal source to account for the energy of the current, in the case in which the hot junction was at or above the neutral temperature.
Consider an elementary couple of two metals A and B for which s has the values s and s" respectively, with junctions at the temperature T and T+dT (absolute), at which the coefficients of the Peltier effect are P and P+dP. Equating the quantity of heat absorbed to the quantity of electrical energy generated, we have by the first law of thermodynamics the relation dE/dT =dP/dT+(s' - s").