Determination of The Peltier Co efficient at a Junction

A copper-iron junction is immersed in a calorimeter containing water. The Cu-Fe junction is joined to a battery, a rheostat, ammeter of a commutator. A current of i ampere, measured by an ammeter A, is passed for t second. The resulting rise in temperature of water in the calorimeter is noted. Let R be the resistance of the junction. If H1 joules are the heat produced, then

        H₁ = i² Rt + πit                                    … (1)
The same current is now passed for the same time in the reverse direction. The rise of temperature is again noted. Let H2 joules be the produced. Then,
        H₂ = i² Rt – πit                                    … (2)
From equs. (1) and (2), we have
    (H₁ – H₂) = 2πit
Or    π = (H₁ – H₂)/2it

Let M be the mass of water in the calorimeter and W the thermal capacity of the calorimeter.

Let θ₁ and θ₂ be the rises in temperature in the two cases respectively.
Then,
            H₁ = (M + W) θ₁ and H₂ = (M + W) θ₂
            (H₁ – _H2) =    (M + W) (θ₁ – θ₂)
                 Π =     (M + W) (θ₁ – θ₂)
                        2it
Hence π is determined from the above relation.


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