Question

In a thermocouple, cold junction is at $0^{\circ }C$, hot junction is at $t^{\circ }C$. The graph drawn between thermo-emf $\left(E\right)$ and temperature of the hot junction $\left(t\right)$ is represented by the equation, $E=at+{bt}^2$. If $a=-224b$, the neutral and the inversion temperatures of the thermocouple respectively, in degree celsius are:

• A. $224,448$
• B. $112,224$
• C. $448,224$
• D. $224,112$

Answer 1

Answer: (B)

$112,224$

The relation is given by,

$E=b{t}^2-224bt$ ; as $a=-224b$ (given)

At neutral temperature, $E$ becomes maximum. Hence, $\frac{dE}{dt}=0$.

$\frac{dE}{dt}=2bt-224b=0$

$t={112}^{0}C$

Also, at inversion temperature, $E=0$. Hence,

$E=b{t}^2-224bt=0$

$t={224}^{0}C$