The thermo emf of a thermocouple varies with temperature θ of the hot junction as E = aθ + bθ² in volts where the ratio a/b is 700. If the cold junction is kept at 0, then the neutral temperature is (a) 1400 (b) 350 (c) 700 (d) No neutral temperature is possible for this termocouple.

Answer: (d). Neutral temperature: (dE)/(dθ) = a + 2bθ = 0 ⇒ θn = -a/2b. θn = -700/2 = -350° C, which is below the cold junction at 0° C. A neutral temperature must lie above the cold-junction temperature, so none is possible: answer (d).

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Electrical Power & Heating Effect

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

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Answer: (d)

Neutral temperature: $\frac{dE}{d\theta} = a + 2b\theta = 0 \Rightarrow \theta_n = -\frac{a}{2b}$ .
$\theta_n = -\frac{700}{2} = -350^\circ$ C, which is below the cold junction at $0^\circ$ C.
A neutral temperature must lie above the cold-junction temperature, so none is possible: answer (d).

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