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)

$E=a\theta +b{\theta }^2$
At neutral temperature $dE/d\theta =0$
$\therefore \frac{dE}{d\theta }=a+2b{\theta }_n=0;{\theta }_n=-\frac{a}{2b}$
Now $\frac{a}{b}=700^{\circ }C$ (given)
${\theta }_n=-700/2=-350^{\circ }C$
Now ${\theta }_c=0^{\circ }C$.
So, ${\theta }_n>0^{\circ }C$
But mathematically ${\theta }_n<0^{\circ }C.$