The thermo emf $E$ in volt of a certain thermo-couple is found to vary with temperature difference $\theta$…

The thermo emf $E$ in volt of a certain thermo-couple is found to vary with temperature difference $\theta$ in ${ }^{\circ} \mathrm{C}$ between the two junctions according to the relation $E=30 \theta-\frac{\theta^2}{15}$ The neutral temperature for the thermo-couple will be
  1. $450^{\circ} \mathrm{C}$
  2. $400^{\circ} \mathrm{C}$
  3. $225^{\circ} \mathrm{C}$
  4. $30^{\circ} \mathrm{C}$

Solution

Given, $\mathrm{E}=30 \theta-\frac{\theta^2}{15}$ At neutral temperature $\begin{aligned} \frac{\mathrm{dE}}{\mathrm{d} \theta} & =0 \\ \therefore \quad 30-\frac{2 \theta}{15} & =0 \\ \theta & =225^{\circ} \mathrm{C} \end{aligned}$

Asked in: NEET 2010 (Mains)

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