Question

The e.m.f. $E$ of a certain thermocouple depends on the temperature difference $\theta$ between its two junctions in accordance with the relation $E=70 \theta-\frac{\theta^{2}}{20}$, where $E$ is in microvolt, $\theta$ in degree celsius and one junction is at zero degree celsius. If $E$ takes value of $\pm 150\, \mu V$, the possible error $\left(\right.$ in $\left.{ }^{\circ} C \right)$, when measuring a temperature of $200^{\circ} C$ is $\pm Z$. Find the value of ' $Z$ '.

Answer 1

$E =70\, \theta-\frac{\theta^{2}}{20}$
$\therefore \frac{ dE }{ d \theta}=70-\frac{2 \theta}{20}$
Here, $dE =\pm 150 \mu V , \theta =200^{\circ} C$
$\therefore \pm \frac{150}{d \theta} =70-\frac{2 \times 200}{20}=50$
$d \theta =\pm \frac{150}{50}$
$=\pm 3$