Question

The thermo emf of a hypothetical thermocouple varies with the temperature e of hot junction as $E=a\theta +{b\theta }^2$ in volts, where the ratio $\frac{a}{b}$ is ${700}^{\circ }C$. If the cold junction is kept at $0^{\circ }C$ then the neutral temperature is

• A. ${700}^{\circ }C$
• B. ${1400}^{\circ }C$
• C. ${390}^{\circ }C$
• D. No neutral temperature is possible for this thermocouple

Answer 1

The correct option is D No neutral temperature is possible for this thermocouple

Neutral temperature is the temperature at which $E$ will have it's maximum value. But clearly this function keeps on increasing for all the positive values of the temperature because

$-\frac{dE}{dt}=a+2b\theta >0$ $\forall$ $\theta \ge 0$

Therefore, there will be no neutral temperature for this thermocouple system.