The e.m.f. E of a certain thermocouple depends on the temperature difference θ between its two junctions in accordance with the relation E=70 θ-(θ2/20), where E is in microvolt, θ in degree celsius and one junction is at zero degree celsius. If E takes value of ± 150 μ V, the possible error (. in . ° C ), when measuring a temperature of 200° C is ± Z. Find the value of ' Z '.

Question

The e.m.f. E of a certain thermocouple depends on the temperature difference θ between its two junctions in accordance with the relation E=70 θ-(θ2/20), where E is in microvolt, θ in degree celsius and one junction is at zero degree celsius. If E takes value of ± 150 μ V, the possible error (. in . ° C ), when measuring a temperature of 200° C is ± Z. Find the value of ' Z '. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

E =70 θ-(θ2/20) ∴ ( dE / d θ)=70-(2 θ/20) Here, dE =± 150 μ V , θ =200° C ∴ ± (150/d θ) =70-(2 × 200/20)=50 d θ =± (150/50) =± 3

E=70θ−20θ2​ ∴dθdE​=70−202θ​ Here, dE=±150μV,θ=200∘C ∴±dθ150​=70−202×200​=50 dθ=±50150​ =±3

$E = 70 θ - \frac{θ ^{2}}{20}$
$∴ \frac{d E}{d θ} = 70 - \frac{2 θ}{20}$
Here, $d E = \pm 150 μ V, θ = 20 0^{\circ} C$
$∴ \pm \frac{150}{d θ} = 70 - \frac{2 \times 200}{20} = 50$
$d θ = \pm \frac{150}{50}$
$= \pm 3$