Q. If the total emf in a thermocouple is a parabolic function expressed as $E = at + \frac{1}{2}\ bt^{2},$ which of the following relation does not hold good?
A) Neutral temperature $t_{n} = - \frac{a}{b}$
B) Temperature of inversion, $t_{i} = - \frac{- 2a}{b}$
C) Thermoelectric power $P = a + bt$
D) $t_{n} = \frac{a}{b}$
Explanation
(a) $E = at + \frac{1}{2}bt^{2}\ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
Differentiating Eq. (i), w.r.t., t
We have
$\frac{dE}{dt} = a + bt$
When $t = t_{n},\ ie,\ $ neural temperature, then
$\frac{dE}{dt} = 0$
$\therefore 0 = a + bt_{n}\ or\ t_{n} = - \frac{a}{b}$
The temperature of inversion
$t_{i} = 2t_{n} = t_{0}$
$\ \ \ \ = 2t_{n} - 0 = - \frac{2a}{b}$
Thermoelectric power
$P = \frac{dE}{dt} = a + bt$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.