Question

The thermo e.m.f. $E$ in volts of a certain thermo-couple is found to vary with temperature difference $\theta$ in ${}^{\circ }C$ between the two junctions according to the relation
$E=30\theta -\frac{{\theta }^2}{15}$. The neutral temperature for the thermo-couple will be

• A. ${225}^{\circ }\text{C}$
• B. ${450}^{\circ }\text{C}$
• C. ${400}^{\circ }\text{C}$
• D. ${30}^{\circ }\text{C}$

Answer 1

The correct option is A ${225}^{\circ }\text{C}$

Given:
$E=30\theta -\frac{{\theta }^2}{15}$
At neutral temperature
$\frac{dE}{d\theta }=0$
$\frac{d}{d\theta }(30\theta -\frac{{\theta }^2}{15})=0$
$\Rightarrow 30-\frac{2\theta }{15}=0$
$\theta ={225}^{\circ }\text{C}$
Hence, option $\left(C\right)$ is correct.