Question

If the total emf in a thermocouple is a parabolic function expressed as $E=at+\frac{1}{2}b{t}^2$ , 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)

$E=at+\frac{1}{2}b{t}^2....$(i)
Differentiating Eq. (i), w.r.t., $t$ we have
$\frac{dE}{dt}=a+bt$
When $t=t_n$, i.e., neutral temperature, then
$\frac{dE}{dt}=0$
$\therefore 0=a+b{t}_n$
or$t_n=-\frac{a}{b}$
The temperature of inversion
$t_i=2t_n-t_0$
$=2t_n-0$
$=-\frac{2a}{b}$
Thermoelectric power
$P=\frac{dE}{dt}=a+bt$