The thermo emf of a thermocouple varies with the temperature $\theta$ of the hot junction as…
The thermo emf of a thermocouple varies with the temperature $\theta$ of the hot junction as $\mathrm{E}=\mathrm{a} \theta+\mathrm{b} \theta^2$ in volts where the ratio $\mathrm{a} / \mathrm{b}$ is $700^{\circ} \mathrm{C}$. If the cold junction is kept at $0^{\circ} \mathrm{C}$, then the neutral temperature is
$700^{\circ} \mathrm{C}$
$350^{\circ} \mathrm{C}$
$1400^{\circ} \mathrm{C}$
no neutral temperature is possible for this thermocouple.
Solution
$E=a \theta+b \theta^2$
At neutral temperature $\mathrm{dE} / \mathrm{d} \theta=0$
$\therefore \frac{\mathrm{dE}}{\mathrm{d} \theta}=\mathrm{a}+2 \mathrm{~b} \theta_{\mathrm{n}}=0 ; \theta_{\mathrm{n}}=-\frac{\mathrm{a}}{2 \mathrm{~b}}$
Now $\frac{a}{b}=700^{\circ} \mathrm{C}$ (given)
$\theta_n=-700 / 2=-350^{\circ} \mathrm{C}$
Now $\theta_c=0^{\circ} \mathrm{C}$.
So, $\theta_n>0^{\circ} \mathrm{C}$
But mathematically $\theta_{\mathrm{n}} < 0^{\circ} \mathrm{C}$.