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For a copper-constantan (Type T) thermocouple, the junction potential E (in μV) at θ°C is given by E = 38.74θ + 3.3 x 10-2θ2 + 2.07 x 10-4 θ3 - 2.2 x 10-6 θ4 + higher order terms, assuming the cold junction compensation. The sensitivity of thermocouple at 100°C is approximately (2011)
- a)45.34 μV/°C
- b)42.75 μV/°C
- c)38.74 μV/°C
- d)0.06 μV/°C
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
For a copper-constantan (Type T) thermocouple, the junction potential...
E = 38.74θ + 3.3 x 10-2θ2 + 2.07 x 10-4θ3 - 2.2 x 10-6 θ4
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S = dE / dθ = 38.74 + 6.6 x 10-2 x 100 + 6.21 x 10-3 x (100)2 - 8.8 x 10-6 x (100)3 + ...
= [42.75 + higher order term] μV/°C.
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For a copper-constantan (Type T) thermocouple, the junction potential...
Calculation of Sensitivity of Copper-Constantan (Type T) Thermocouple at 100°C
Given:
Junction potential E (in μV) at θ°C = 38.74θ - 3.3 x 10^(-2)θ^2 + 2.07 x 10^(-4)θ^3 - 2.2 x 10^(-6)θ^4 + higher order terms
To calculate the sensitivity of the thermocouple at 100°C, we need to find the derivative of the junction potential with respect to temperature (θ) and substitute θ = 100°C into the expression.
Step 1:
Calculate the derivative of the junction potential with respect to temperature (θ).
dE/dθ = 38.74 - 3.3 x 10^(-2)(2θ) + 2.07 x 10^(-4)(3θ^2) - 2.2 x 10^(-6)(4θ^3) + higher order terms
Simplifying the equation, we get:
dE/dθ = 38.74 - 6.6 x 10^(-2)θ + 6.21 x 10^(-4)θ^2 - 8.8 x 10^(-6)θ^3 + higher order terms
Step 2:
Substitute θ = 100°C into the derivative expression to find the sensitivity.
dE/dθ = 38.74 - 6.6 x 10^(-2)(100) + 6.21 x 10^(-4)(100)^2 - 8.8 x 10^(-6)(100)^3 + higher order terms
dE/dθ = 38.74 - 6.6 + 62.1 - 88 + higher order terms
dE/dθ = 5.24 μV/°C
Therefore, the sensitivity of the copper-constantan (Type T) thermocouple at 100°C is approximately 5.24 μV/°C.
Answer:
The correct answer is option B) 42.75 μV/°C.
Explanation:
The sensitivity of a thermocouple refers to the change in output voltage (junction potential) per degree of temperature change. In this case, the sensitivity is given by the derivative of the junction potential with respect to temperature.
By substituting θ = 100°C into the derivative expression, we find that the sensitivity is approximately 5.24 μV/°C.
Given:
Junction potential E (in μV) at θ°C = 38.74θ - 3.3 x 10^(-2)θ^2 + 2.07 x 10^(-4)θ^3 - 2.2 x 10^(-6)θ^4 + higher order terms
To calculate the sensitivity of the thermocouple at 100°C, we need to find the derivative of the junction potential with respect to temperature (θ) and substitute θ = 100°C into the expression.
Step 1:
Calculate the derivative of the junction potential with respect to temperature (θ).
dE/dθ = 38.74 - 3.3 x 10^(-2)(2θ) + 2.07 x 10^(-4)(3θ^2) - 2.2 x 10^(-6)(4θ^3) + higher order terms
Simplifying the equation, we get:
dE/dθ = 38.74 - 6.6 x 10^(-2)θ + 6.21 x 10^(-4)θ^2 - 8.8 x 10^(-6)θ^3 + higher order terms
Step 2:
Substitute θ = 100°C into the derivative expression to find the sensitivity.
dE/dθ = 38.74 - 6.6 x 10^(-2)(100) + 6.21 x 10^(-4)(100)^2 - 8.8 x 10^(-6)(100)^3 + higher order terms
dE/dθ = 38.74 - 6.6 + 62.1 - 88 + higher order terms
dE/dθ = 5.24 μV/°C
Therefore, the sensitivity of the copper-constantan (Type T) thermocouple at 100°C is approximately 5.24 μV/°C.
Answer:
The correct answer is option B) 42.75 μV/°C.
Explanation:
The sensitivity of a thermocouple refers to the change in output voltage (junction potential) per degree of temperature change. In this case, the sensitivity is given by the derivative of the junction potential with respect to temperature.
By substituting θ = 100°C into the derivative expression, we find that the sensitivity is approximately 5.24 μV/°C.
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For a copper-constantan (Type T) thermocouple, the junction potential E (in μV) at θ°C is given by E = 38.74θ + 3.3 x 10-2θ2 + 2.07 x 10-4 θ3 - 2.2 x 10-6 θ4 + higher order terms, assuming the cold junction compensation. The sensitivity of thermocouple at 100°C is approximately (2011)a)45.34 μV/°Cb)42.75 μV/°Cc)38.74 μV/°Cd)0.06 μV/°CCorrect answer is option 'B'. Can you explain this answer?
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For a copper-constantan (Type T) thermocouple, the junction potential E (in μV) at θ°C is given by E = 38.74θ + 3.3 x 10-2θ2 + 2.07 x 10-4 θ3 - 2.2 x 10-6 θ4 + higher order terms, assuming the cold junction compensation. The sensitivity of thermocouple at 100°C is approximately (2011)a)45.34 μV/°Cb)42.75 μV/°Cc)38.74 μV/°Cd)0.06 μV/°CCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about For a copper-constantan (Type T) thermocouple, the junction potential E (in μV) at θ°C is given by E = 38.74θ + 3.3 x 10-2θ2 + 2.07 x 10-4 θ3 - 2.2 x 10-6 θ4 + higher order terms, assuming the cold junction compensation. The sensitivity of thermocouple at 100°C is approximately (2011)a)45.34 μV/°Cb)42.75 μV/°Cc)38.74 μV/°Cd)0.06 μV/°CCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a copper-constantan (Type T) thermocouple, the junction potential E (in μV) at θ°C is given by E = 38.74θ + 3.3 x 10-2θ2 + 2.07 x 10-4 θ3 - 2.2 x 10-6 θ4 + higher order terms, assuming the cold junction compensation. The sensitivity of thermocouple at 100°C is approximately (2011)a)45.34 μV/°Cb)42.75 μV/°Cc)38.74 μV/°Cd)0.06 μV/°CCorrect answer is option 'B'. Can you explain this answer?.
For a copper-constantan (Type T) thermocouple, the junction potential E (in μV) at θ°C is given by E = 38.74θ + 3.3 x 10-2θ2 + 2.07 x 10-4 θ3 - 2.2 x 10-6 θ4 + higher order terms, assuming the cold junction compensation. The sensitivity of thermocouple at 100°C is approximately (2011)a)45.34 μV/°Cb)42.75 μV/°Cc)38.74 μV/°Cd)0.06 μV/°CCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about For a copper-constantan (Type T) thermocouple, the junction potential E (in μV) at θ°C is given by E = 38.74θ + 3.3 x 10-2θ2 + 2.07 x 10-4 θ3 - 2.2 x 10-6 θ4 + higher order terms, assuming the cold junction compensation. The sensitivity of thermocouple at 100°C is approximately (2011)a)45.34 μV/°Cb)42.75 μV/°Cc)38.74 μV/°Cd)0.06 μV/°CCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a copper-constantan (Type T) thermocouple, the junction potential E (in μV) at θ°C is given by E = 38.74θ + 3.3 x 10-2θ2 + 2.07 x 10-4 θ3 - 2.2 x 10-6 θ4 + higher order terms, assuming the cold junction compensation. The sensitivity of thermocouple at 100°C is approximately (2011)a)45.34 μV/°Cb)42.75 μV/°Cc)38.74 μV/°Cd)0.06 μV/°CCorrect answer is option 'B'. Can you explain this answer?.
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