Question

If the total emf in a thermocouple is a parabolic function expressed as \( E = at + \frac{1}{2}bt^2 \), which of the following relations does not hold good

• A. normal temperature \( t_0 = \frac{a}{b} \)
• B. temperature of inversion \( t_1 = \frac{-2a}{b} \)
• C. thermo-electric power \( p = a + bt \)
• D. \( t_2 = \frac{a}{b} \)

Hint:

For parabolic EMF functions, the normal and inversion temperatures can be derived by differentiating the function and solving for zero slope.

Answer 1

The Correct Option is D

Step 1: Analyzing the given function.
The thermo-electric power is the rate of change of the EMF with respect to temperature: \[ p = \frac{dE}{dt} = a + bt \] The normal temperature is given by \( t_0 = \frac{a}{b} \), and the temperature of inversion is \( t_1 = \frac{-2a}{b} \). The relation in option (D) is incorrect.

Step 2: Conclusion.
Thus, the correct answer is option (D).

Final Answer: \[ \boxed{\text{(D) } t_2 = \frac{a}{b}} \]