For a copper-constantan type T thermocouple- the junction potential E in - V at 0oC is given byE-42-58-5-6- 10-2- 2-2-35- 10-4-3-2-1- 10-6-4- higher order terms- Assuming the cold junction compensation- The sensitivity of thermocouple at 100oC is muV-oC

Sensitivity =dEdθ =ddθ[42.58θ+5.6× 10^ 2θ ^2+2.35× 10^ 4θ^3 2.1× 10^ 6θ^4]μ V =42.58+2× 5.6× 10^2θ +2.35× 10^ 4× 3×θ^2 2.1× 4× 10^ 6θ ^3 μ V/^oC =42.58+11.2+ ...

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Standard XII

Physics

Mutual Induction

For a copper-...

Question

For a copper-constantan (type T) thermocouple, the junction potential $E ($ in $μ V)$ at $0^{o} C$ is given by
$E = 42.58 θ + 5.6 \times 10^{- 2} θ^{2} + 2.35 \times 10^{- 4} θ^{3} - 2.1 \times 10^{- 6} θ^{4} + h i g h e r o r d e r t e r m s .$ Assuming the cold junction compensation. The sensitivity of thermocouple at $100^{o} C$ is ____ $m u V /^{o} C$

52.4

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42.4

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44.4

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54.4

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Solution

The correct option is A $52.4$
$S e n s i t i v i t y = \frac{d E}{d θ}$

$= \frac{d}{d θ} [42.58 θ + 5.6 \times 10^{- 2} θ^{2} + 2.35 \times 10^{- 4} θ^{3} - 2.1 \times 10^{- 6} θ^{4}] μ V$

$= 42.58 + 2 \times 5.6 \times 10^{2} θ + 2.35 \times 10^{- 4} \times 3 \times θ^{2} - 2.1 \times 4 \times 10^{- 6} θ^{3} μ V /^{o} C$

$= 42.58 + 11.2 + 7.05 - 8.4$

$= 52.4 μ V /^{o} C$

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For a copper-constantan (type T) thermocouple, the junction potential E (in μV) at 0oC is given by E=42.58θ+5.6×10−2θ2+2.35×10−4θ3−2.1×10−6θ4+higher order terms. Assuming the cold junction compensation. The sensitivity of thermocouple at 100oC is ____ muV/oC

The correct option is A 52.4Sensitivity=dEdθ =ddθ[42.58θ+5.6×10−2θ2+2.35×10−4θ3−2.1×10−6θ4]μV =42.58+2×5.6×102θ+2.35×10−4×3×θ2−2.1×4×10−6θ3μV/oC =42.58+11.2+7.05−8.4 =52.4 μV/oC