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 σ_x and σ_y 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 + ∫ σ_x dT = - ∫σ_y dT
         = π₁ – π₂ + ∫ (σ_x - σ_y) 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.


For more help in Total EMF in a Thermo-couple click the button below to submit your homework assignment