The thermo emf of a hypothetical thermocouple varies with the temperature θ of hot junction as E = $a θ + b θ^{2}$ in volts, where the ratio $\frac{a}{b}$ is 700^o C. If the cold junction is kept at 0^o C, then the neutral temperature is

700^o C

1400^o C

390^o C

no neutral temperature is possible for this thermocouple

Solution

no neutral temperature is possible for this thermocouple

When two wires composed of dissimilar metals are joined at both ends and one of the ends is heated, there is a continuous current which flows in the thermoelectric circuit.

The emf set in the thermocouple, when its two junctions are kept at different temperatures is called thermo e.m.f

Given:-

E = aθ + bθ²

$P = \frac{dE}{dt}$

= $\frac{d}{dθ} (aθ + {bθ}^{2})$

P = a + 2 bθ

At θ = T_n ,P = 0

⇒ 0 = a + 2 b T

⇒ T_n = $- \frac{a}{2 b}$

⇒ T_n = - $\frac{700^{o}}{2}$

T_n = - 350^o C

The temperature of the hot junction of a thermocouple at which the elctromotive force on the thermocouple attains its maximum value, when the cold junction is maintained at constant temperature of 0^o C , called neutral temperature.

But neutral temperature can never be negative ( less than zero)

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