Question

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

• A. ${700}^{0}C$
• B. ${350}^{0}C$
• C. ${1400}^{0}C$
• D. no neutral temperature is possible for this thermocouple

Answer 1

Answer: (D)

no neutral temperature is possible for this thermocouple

The neutral temperature is the temperature corresponding to maximum thermo-emf.

At neutral temperature $\frac{dE}{d\theta }=0$

Here, $\frac{dE}{d\theta }=0$ implies

$a+2b\theta =0$

on solving,

$\theta =\frac{-2b}{a}$

Given $\frac{a}{b}={700}^{\circ }C$

gives $\theta$

a negative value which is not possible

(Because $\theta$ is the temperature difference between hot and cold junction which should be positive)