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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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