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The following data pertains to the junction of a thermocouple wire used to measure the temperature of the gas stream. Density = 8500 kg/m3, specific heat = 325 J/kg K, thermal conductivity = 40 W/m K and the heat transfer coefficient between the junction and gas = 215 W/m2 K.
If thermocouple junction can be approximated as a 1 mm diameter sphere, determine how long it will take for the thermocouple to read 99% of the initial temperature difference
  • a)
    9.86 seconds
  • b)
    8.86 seconds
  • c)
    7.86 seconds
  • d)
    6.86 seconds
Correct answer is option 'A'. Can you explain this answer?
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The following data pertains to the junction of a thermocouple wire us...
T – ta / tI – ta = exponential (- p V c T / h A).
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The following data pertains to the junction of a thermocouple wire us...
Given data:
Density (ρ) = 8500 kg/m³
Specific heat (c) = 325 J/kg K
Thermal conductivity (k) = 40 W/m K
Heat transfer coefficient (h) = 215 W/m² K
Diameter of thermocouple junction (d) = 1 mm

To find:
Time taken for the thermocouple to read 99% of the initial temperature difference.

Solution:
The time taken for the thermocouple to read 99% of the initial temperature difference can be calculated using the following formula:

τ = (ρ * c * V) / (h * A)

where,
τ = time constant (s)
V = volume of the thermocouple junction (m³)
A = surface area of the thermocouple junction (m²)

Volume of the thermocouple junction:
V = (4/3) * π * (d/2)³
V = (4/3) * π * (0.001/2)³
V = 5.24 x 10^-10 m³

Surface area of the thermocouple junction:
A = π * d²
A = π * (0.001)²
A = 7.85 x 10^-7 m²

Time constant:
τ = (ρ * c * V) / (h * A)
τ = (8500 * 325 * 5.24 x 10^-10) / (215 * 7.85 x 10^-7)
τ = 9.86 seconds (approx)

Therefore, the time taken for the thermocouple to read 99% of the initial temperature difference is approximately 9.86 seconds. Hence, option (A) is the correct answer.
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The following data pertains to the junction of a thermocouple wire used to measure the temperature of the gas stream. Density = 8500 kg/m3, specific heat = 325 J/kg K, thermal conductivity = 40 W/m K and the heat transfer coefficient between the junction and gas = 215 W/m2 K.If thermocouple junction can be approximated as a 1 mm diameter sphere, determine how long it will take for the thermocouple to read 99% of the initial temperature differencea)9.86 secondsb)8.86 secondsc)7.86 secondsd)6.86 secondsCorrect answer is option 'A'. Can you explain this answer?
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The following data pertains to the junction of a thermocouple wire used to measure the temperature of the gas stream. Density = 8500 kg/m3, specific heat = 325 J/kg K, thermal conductivity = 40 W/m K and the heat transfer coefficient between the junction and gas = 215 W/m2 K.If thermocouple junction can be approximated as a 1 mm diameter sphere, determine how long it will take for the thermocouple to read 99% of the initial temperature differencea)9.86 secondsb)8.86 secondsc)7.86 secondsd)6.86 secondsCorrect answer is option 'A'. 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 The following data pertains to the junction of a thermocouple wire used to measure the temperature of the gas stream. Density = 8500 kg/m3, specific heat = 325 J/kg K, thermal conductivity = 40 W/m K and the heat transfer coefficient between the junction and gas = 215 W/m2 K.If thermocouple junction can be approximated as a 1 mm diameter sphere, determine how long it will take for the thermocouple to read 99% of the initial temperature differencea)9.86 secondsb)8.86 secondsc)7.86 secondsd)6.86 secondsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The following data pertains to the junction of a thermocouple wire used to measure the temperature of the gas stream. Density = 8500 kg/m3, specific heat = 325 J/kg K, thermal conductivity = 40 W/m K and the heat transfer coefficient between the junction and gas = 215 W/m2 K.If thermocouple junction can be approximated as a 1 mm diameter sphere, determine how long it will take for the thermocouple to read 99% of the initial temperature differencea)9.86 secondsb)8.86 secondsc)7.86 secondsd)6.86 secondsCorrect answer is option 'A'. Can you explain this answer?.
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