Question

The emf of a thermocouple, cold junction of which is kept at $-{300}^o$c is given by $E=40t+\frac{1}{10}{t}^2$. The temperature of inversion of thermocouple will be.

• A. ${200}^o$C
• B. ${400}^o$C
• C. $-{200}^o$C
• D. $-{100}^o$C

Answer 1

Answer: (C)

$-{200}^o$C

$E=40t+\frac{1}{20}{t}^2$ at inversion E will be minimum.

$\frac{dE}{dt}=0$

$\Rightarrow \frac{d}{dt}\left[40t+\frac{1}{10}{t}^2\right]=0$

$40+\frac{1}{5}t=0$
$t=-40\times 5=-{200}^o$C.