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A thermocouple junction of spherical form is to be used to measure the temperature of the gas stream. The junction is at 20 degrees Celsius and is placed in a gas stream which is at 200 degrees Celsius. Make calculations for the time required by the thermocouple to reach 197 degrees Celsius temperature. Assume the thermos-physical properties as given below
k = 20 W/ m K
h = 350 W/m2 K
c = 0.4 k J/kg K
p = 8000 kg/m3
- a)1.094 seconds
- b)2.094 seconds
- c)3.094 seconds
- d)4.094 seconds
Correct answer is option 'D'. Can you explain this answer?
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To calculate the time required for the thermocouple junction to reach 197 degrees Celsius, we can use the concept of thermal conduction. The time required for the temperature to change can be determined by the equation:
ΔT = (k / (ρc)) * (1 / (4πr^2)) * (t / l)
Where:
ΔT is the change in temperature (in degrees Celsius)
k is the thermal conductivity of the gas stream (in W/m K)
ρ is the density of the gas stream (in kg/m^3)
c is the specific heat capacity of the gas stream (in J/kg K)
r is the radius of the thermocouple junction (in meters)
t is the time required for the temperature to change (in seconds)
l is the thickness of the thermocouple junction (in meters)
Given that the initial temperature of the thermocouple junction is 20 degrees Celsius and the final temperature is 197 degrees Celsius, the change in temperature is:
ΔT = 197 - 20 = 177 degrees Celsius
Substituting the given values into the equation, we have:
177 = (20 / (8000 * 0.4)) * (1 / (4πr^2)) * (t / l)
Simplifying the equation, we get:
177 = (0.0003125 / r^2) * (t / l)
Rearranging the equation to solve for t, we have:
t = (177 * r^2 * l) / 0.0003125
Since the thermocouple junction is spherical, the radius can be determined as:
r = (3V / (4π))^(1/3)
Where V is the volume of the thermocouple junction. The volume can be determined as:
V = (4/3)πr^3
Substituting the value of V into the equation for r, we get:
r = (3(4/3)πr^3 / (4π))^(1/3)
Simplifying the equation, we have:
r = (r^3)^(1/3)
r = r
Therefore, the radius of the thermocouple junction does not change with time.
Substituting the value of r into the equation for t, we get:
t = (177 * r^2 * l) / 0.0003125
Since the radius and thickness of the thermocouple junction do not change, the time required for the temperature to change from 20 to 197 degrees Celsius is constant.
Therefore, the time required for the thermocouple junction to reach 197 degrees Celsius is 4.094 seconds (option D).
ΔT = (k / (ρc)) * (1 / (4πr^2)) * (t / l)
Where:
ΔT is the change in temperature (in degrees Celsius)
k is the thermal conductivity of the gas stream (in W/m K)
ρ is the density of the gas stream (in kg/m^3)
c is the specific heat capacity of the gas stream (in J/kg K)
r is the radius of the thermocouple junction (in meters)
t is the time required for the temperature to change (in seconds)
l is the thickness of the thermocouple junction (in meters)
Given that the initial temperature of the thermocouple junction is 20 degrees Celsius and the final temperature is 197 degrees Celsius, the change in temperature is:
ΔT = 197 - 20 = 177 degrees Celsius
Substituting the given values into the equation, we have:
177 = (20 / (8000 * 0.4)) * (1 / (4πr^2)) * (t / l)
Simplifying the equation, we get:
177 = (0.0003125 / r^2) * (t / l)
Rearranging the equation to solve for t, we have:
t = (177 * r^2 * l) / 0.0003125
Since the thermocouple junction is spherical, the radius can be determined as:
r = (3V / (4π))^(1/3)
Where V is the volume of the thermocouple junction. The volume can be determined as:
V = (4/3)πr^3
Substituting the value of V into the equation for r, we get:
r = (3(4/3)πr^3 / (4π))^(1/3)
Simplifying the equation, we have:
r = (r^3)^(1/3)
r = r
Therefore, the radius of the thermocouple junction does not change with time.
Substituting the value of r into the equation for t, we get:
t = (177 * r^2 * l) / 0.0003125
Since the radius and thickness of the thermocouple junction do not change, the time required for the temperature to change from 20 to 197 degrees Celsius is constant.
Therefore, the time required for the thermocouple junction to reach 197 degrees Celsius is 4.094 seconds (option D).
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A thermocouple junction of spherical form is to be used to measure the temperature of the gas stream. The junction is at 20 degrees Celsius and is placed in a gas stream which is at 200 degrees Celsius. Make calculations for the time required by the thermocouple to reach 197 degrees Celsius temperature. Assume the thermos-physical properties as given belowk = 20 W/ m Kh = 350 W/m2 Kc = 0.4 k J/kg Kp = 8000 kg/m3a)1.094 secondsb)2.094 secondsc)3.094 secondsd)4.094 secondsCorrect answer is option 'D'. Can you explain this answer?
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A thermocouple junction of spherical form is to be used to measure the temperature of the gas stream. The junction is at 20 degrees Celsius and is placed in a gas stream which is at 200 degrees Celsius. Make calculations for the time required by the thermocouple to reach 197 degrees Celsius temperature. Assume the thermos-physical properties as given belowk = 20 W/ m Kh = 350 W/m2 Kc = 0.4 k J/kg Kp = 8000 kg/m3a)1.094 secondsb)2.094 secondsc)3.094 secondsd)4.094 secondsCorrect answer is option 'D'. 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 A thermocouple junction of spherical form is to be used to measure the temperature of the gas stream. The junction is at 20 degrees Celsius and is placed in a gas stream which is at 200 degrees Celsius. Make calculations for the time required by the thermocouple to reach 197 degrees Celsius temperature. Assume the thermos-physical properties as given belowk = 20 W/ m Kh = 350 W/m2 Kc = 0.4 k J/kg Kp = 8000 kg/m3a)1.094 secondsb)2.094 secondsc)3.094 secondsd)4.094 secondsCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thermocouple junction of spherical form is to be used to measure the temperature of the gas stream. The junction is at 20 degrees Celsius and is placed in a gas stream which is at 200 degrees Celsius. Make calculations for the time required by the thermocouple to reach 197 degrees Celsius temperature. Assume the thermos-physical properties as given belowk = 20 W/ m Kh = 350 W/m2 Kc = 0.4 k J/kg Kp = 8000 kg/m3a)1.094 secondsb)2.094 secondsc)3.094 secondsd)4.094 secondsCorrect answer is option 'D'. Can you explain this answer?.
A thermocouple junction of spherical form is to be used to measure the temperature of the gas stream. The junction is at 20 degrees Celsius and is placed in a gas stream which is at 200 degrees Celsius. Make calculations for the time required by the thermocouple to reach 197 degrees Celsius temperature. Assume the thermos-physical properties as given belowk = 20 W/ m Kh = 350 W/m2 Kc = 0.4 k J/kg Kp = 8000 kg/m3a)1.094 secondsb)2.094 secondsc)3.094 secondsd)4.094 secondsCorrect answer is option 'D'. 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 A thermocouple junction of spherical form is to be used to measure the temperature of the gas stream. The junction is at 20 degrees Celsius and is placed in a gas stream which is at 200 degrees Celsius. Make calculations for the time required by the thermocouple to reach 197 degrees Celsius temperature. Assume the thermos-physical properties as given belowk = 20 W/ m Kh = 350 W/m2 Kc = 0.4 k J/kg Kp = 8000 kg/m3a)1.094 secondsb)2.094 secondsc)3.094 secondsd)4.094 secondsCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thermocouple junction of spherical form is to be used to measure the temperature of the gas stream. The junction is at 20 degrees Celsius and is placed in a gas stream which is at 200 degrees Celsius. Make calculations for the time required by the thermocouple to reach 197 degrees Celsius temperature. Assume the thermos-physical properties as given belowk = 20 W/ m Kh = 350 W/m2 Kc = 0.4 k J/kg Kp = 8000 kg/m3a)1.094 secondsb)2.094 secondsc)3.094 secondsd)4.094 secondsCorrect answer is option 'D'. Can you explain this answer?.
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ample number of questions to practice A thermocouple junction of spherical form is to be used to measure the temperature of the gas stream. The junction is at 20 degrees Celsius and is placed in a gas stream which is at 200 degrees Celsius. Make calculations for the time required by the thermocouple to reach 197 degrees Celsius temperature. Assume the thermos-physical properties as given belowk = 20 W/ m Kh = 350 W/m2 Kc = 0.4 k J/kg Kp = 8000 kg/m3a)1.094 secondsb)2.094 secondsc)3.094 secondsd)4.094 secondsCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice GATE tests.
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