Question

The thermo-emf of a thermocouple varies with the temperature $ \theta $ of the hot junction as $ E=a\theta +b{{\theta }^{2}} $ in volts where the ratio a/b is $ 700{}^\circ C $ . If the cold junction is kept at $ 0{}^\circ C, $ then the neutral temperature is

• A. $ 700{}^\circ C $
• B. $ 350{}^\circ C $
• C. $ 1400{}^\circ C $
• D. no neutral temperature is possible for this thermocouple

Answer 1

Answer: (D)

$ 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;.