Question

The cold junction of a thermocouple is at ${{0}^{{}^\circ }}C$. The thermo emf produced in the thermocouple is given by an equation $E=16T-0.04{{T}^{2}}V$, where T is the temperature of the hot junction. The temperature of inversion and neutral temperature of the thermocouple are:
(A) ${{200}^{{}^\circ }}C,{{400}^{{}^\circ }}C$
(B) ${{400}^{{}^\circ }}C,{{200}^{{}^\circ }}C$
(C) ${{200}^{{}^\circ }}C,{{300}^{{}^\circ }}C$
(D) ${{300}^{{}^\circ }}C,{{200}^{{}^\circ }}C$

Answer 1

Hint To answer this question we should begin the answer in two parts. At first with the help of the equation that is mentioned in the questions, we can find out the temperature of the inversion. Then for finding the temperature of the neutral we need to replace the value of the temperature, after performing a differentiation. At the end we will be with two of the required temperatures.

Complete step by step answer
In the given question it is given that $E=16T-0.04{{T}^{2}}V$.
We know that for the inversion temperature,
$T={{T}_{i}}$ and E=0
So we can say that:
$16-0.04(2{{T}_{n}})=0$
$\Rightarrow {{T}_{n}}={{200}^{{}^\circ }}C$
Now for the neutral temperature we can write that:
$T={{T}_{{{n}_{{}}}}}$
$\Rightarrow \dfrac{dE}{dT}=0$
So now it is that:
$16-0.04(2{{T}_{n}})=0$
$\Rightarrow {{T}_{n}}={{200}^{{}^\circ }}C$
Hence we can say that the temperature of inversion and neutral temperature of the

thermocouple are ${{400}^{{}^\circ }}C,{{200}^{{}^\circ }}C$. So option B is correct.

Note In this question we have come across two terms. For better understanding we should be defining both the terms. First let us define the term inversion temperature. By inversion temperature we mean the temperature at which the emf of the thermo will change its sign. The emf value will be zero at the hotter region.
Next we have the neutral temperature. By neutral temperature of a thermocouple we mean the temperature at which the emf of the thermo is maximum.