The cold junction of a thermocouple is at $0^{\circ} \mathrm{C}$. The thermo e.m.f produced in the…
The cold junction of a thermocouple is at $0^{\circ} \mathrm{C}$. The thermo e.m.f produced in the thermocouple is given by an equation $E=16 T-0.04 T^2$, where $T$ is the temperature of the hot junction. The temperature of inversion and neutral temperature of the thermocouple are
$200^{\circ} \mathrm{C} ; 400^{\circ} \mathrm{C}$
$400^{\circ} \mathrm{C} ; 200^{\circ} \mathrm{C}$
$200^{\circ} \mathrm{C} ; 300^{\circ} \mathrm{C}$
$300^{\circ} \mathrm{C} ; 200^{\circ} \mathrm{C}$
Solution
Thermo emf $E=16 T-0.04 T^2$
At inversion temperature $\left(T i\right), E=0$
$
\therefore \quad \begin{aligned}
0 & =16 T_i-0.04 T_i^2 \\
16 T i & =0.04 T_i^2 \\
T i & =\frac{16}{0.04}=400^{\circ} \mathrm{C}
\end{aligned}
$
Neutral temperature $T_n=\frac{T i+T}{2}$
$T=$ Temperature of cold end
$
T_n=\frac{400+0}{2}=200^{\circ} \mathrm{C}
$