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 $700{}^{\circ }C$ . If the cold junction is kept at $0{}^{\circ }C,$ then the neutral temperature is

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

Answer 1

Answer: (D)

$E=a\theta +b{\theta }^2$ (given) For neutral temperature $({\theta }_n),\frac{dE}{d\theta }=0$ $\Rightarrow$ $a+2b{\theta }_n=0$ $\Rightarrow$ ${\theta }_n=-\frac{a}{2b}$ $\therefore$ ${\theta }_n=-\frac{700}{2}$ $\left(\because \frac{a}{b}=700{}^{\circ }C\right)$ $=-350{}^{\circ }C<0{}^{\circ }C$ But neutral temperature can never be negative (less than zero) i.e., ${\theta }_n<|0{}^{\circ }C$ . Hence, no neutral temperature is possible for this thermocouple;.