question_answer

The temperature of the cold junction of a thermocouple is \[0{}^\circ C\] and the temperature of the hot junction is \[T{}^\circ C\]. The relation for the thermo emf is given by, \[E=AT-\frac{1}{2}B{{T}^{2}}\] (when A = 16 and B - 0.08). The temperature of inversion will be:

A) \[500{}^\circ C\]

B) \[460{}^\circ C\]

C) \[600{}^\circ C\]

D) \[400{}^\circ C\]

Correct Answer: D

Solution :

                Key Idea: At the temperature of inversion the thermo emf is zero. Let temperature of cold junction be \[\frac{1}{4}\] and that of hot junction be \[{{s}^{2}}\]. The relation for thermo emf is given by \[{{m}_{1}},{{m}_{2}}\] Given,     \[{{m}_{3}}\] \[\frac{1}{{{m}_{1}}}:\frac{1}{{{m}_{2}}}:\frac{1}{{{m}_{3}}}\]  \[1:1:1\] Since, emf is zero at temperature of inversion we have \[{{m}_{1}}:2{{m}_{2}}:3{{m}_{3}}\] \[{{m}_{1}}:{{m}_{2}}:{{m}_{3}}\]                    \[\overset{0}{\mathop{A}}\,\]