A) \[700{}^\circ C\]
B) \[350{}^\circ C\]
C) \[1400{}^\circ C\]
D) no neutral temperature is possible for this thermocouple
Correct Answer: D
Solution :
\[E=a\theta +b{{\theta }^{2}}\] (given) For neutral temperature \[({{\theta }_{n}}),\frac{dE}{d\theta }=0\] \[\Rightarrow \] \[a+2b{{\theta }_{n}}=0\] \[\Rightarrow \] \[{{\theta }_{n}}=-\frac{a}{2b}\] \[\therefore \] \[{{\theta }_{n}}=-\frac{700}{2}\] \[\left( \because \frac{a}{b}=700{}^\circ C \right)\] \[=-350{}^\circ C<0{}^\circ C\] But neutral temperature can never be negative (less than zero) i.e.,\[{{\theta }_{n}}<|0{}^\circ C\]. Hence, no neutral temperature is possible for this thermocouple;.
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