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Total EMF in a Thermo-couple

Consider a thermo-couple made of two dissimilar metals X and Y. Let the temperatures of the hot and cold junctions be T1 and T2 respectively. Let the current be positive from X to Y at the hot junction. Let π1 and π2 be the Peltier coefficient at the junctions at T1 and T2 respectively. Let σx and σy by the Thomson coefficients for the metal X and Y respectively. When the electric charge flows in the thermocouple, the heat is absorbed and evolved at the junctions due to Peltier effect and all along the conductor due to Thomson effect. The total emf round the circuit ε is the energy gained by unit charge when passing round the circuit.

The total emf responsible for the thermocurrent must be the sum of potentials due to Peltier and Thomson effects.
     . :    ε = Sum of pds. Across various parts of the circuit
         = π1 – π2 + ∫ σx dT = - ∫σy dT
         = π1 – π2 + ∫ (σx - σy) dT                                … (1)

It is equal to the total Seebeck emf available in the circuit.
Eq. (1) is the expression for the total thermo-emf developed in a thermocouple.

Total EMF in a Thermo couple

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