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

Question

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

Dr. Abubacker · Accepted Answer

(d) $E = a	heta + b	heta^{2}$ (given)
For neutral temperature $\left( 	heta_{n} ight),\frac{dE}{d	heta} = 0$
$\Rightarrow \ \ a + 2b\ 	heta_{n} = 0$
$\Rightarrow \ 	heta_{n} = - \frac{a}{2b}$
$	herefore\ 	heta_{n} = - \frac{700}{2}\ \ \ \ \ \ \ \ \ \ \left( \because\frac{a}{b} = 700℃ ight)$
$\ \ \ \ \ \ \ \ \ \ \  = - 350℃ < 0℃$
But neutral temperature can never be negative (less than zero), $ie,\ 	heta_{n} 
less 0℃.$
Hence, no neutral temperature is possible for this thermocouple.

Q. 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 $700℃.$ If the cold junction is kept at $0℃,$ then the neutral temperature is

Explanation

Reviewed by Dr. Abubacker

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