explain Variation of Thermo emf with temperature

To study the variation of thermo emf with temperature, an iron-copper thermocouple with galvanometer is taken whose one junction is immersed into oil and another at melting ice as shown in figure.

Initially when both junctions are at the same temperature, galvanometer shows no deflection i.e. no emf is developed. As the temperature of oil bath is increased keeping the cold junction at steady temperature, the thermo emf increases till it attains the maximum point.

On further raising the temperature of hot junction, the thermo emf decreases and becomes zero at certain temperature called temperature of inversion (θi). As the temperature is further increased beyond θi, thermo emf is reversed.

Hence, the relation between thermo emf and temperature difference θ between hot and cold junction is given by,

$E = \alpha θ + \frac 12 \beta θ^2$

Where $\alpha$ and $\beta$ are constant.

Moreover, if $θ_c$ is the temperature of cold junction then,

$θ_i - θ_n = θ_n - θ_c$
or, $θ_n = \frac{θ_i + θ_c}{2}$

Hence, the neutral temperature is the average value of inversion temperature and temperature of cold junction.