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. neutral temperature $t_n = -a/b$
• B. temperature of inversion $t_i = -2a/b$
• C. thermo-electric power $p = a + bt$
• D. $t_n = \frac{a}{b}$

Answer 1

Answer: (D)

$E=a t+\frac{1}{2} b t^{2}....$(i)
Differentiating Eq. (i), w.r.t., $t$ we have
$\frac{d E}{d t}=a+b t$
When $t=t_{n}$, i.e., neutral temperature, then
$\frac{d E}{d t}=0$
$\therefore 0=a+b t_{n}$
or$t_{n}=-\frac{a}{b}$
The temperature of inversion
$t_{i} =2 t_{n}-t_{0} $
$=2 t_{n}-0 $
$=-\frac{2 a}{b}$
Thermoelectric power
$P=\frac{d E}{d t}=a+b t$