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A thermocouple is suddenly immersed in a medium of high temperature. The approximate
time taken by the thermocouple to reach 98% of the steady-state value is
- a)equal to the time constant of the thermocouple
- b)equal to twice the value of the time constant of the thermocouple
- c)equal to four times the value of the time constant of the thermocouple
- d)independent of the time constant
Correct answer is option 'C'. Can you explain this answer?
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A thermocouple is suddenly immersed in a medium of high temperature. ...
The output at line t
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c (t) = c0 (1 – e– t/T)
For, c (t) = 0.98 C0
we have, 0.98 C0 = C0 (1 – e– t/T)
or t = 4 T
Most Upvoted Answer
A thermocouple is suddenly immersed in a medium of high temperature. ...
Explanation:
Time Constant:
The time constant of a thermocouple is a measure of how quickly it responds to changes in temperature. It is defined as the time it takes for the thermocouple to reach approximately 63.2% of its steady-state value when subjected to a step change in temperature.
Response of Thermocouple:
When a thermocouple is suddenly immersed in a medium of high temperature, it tends to reach a steady-state value over time. The response of the thermocouple can be represented by an exponential function.
Formula:
The response of a thermocouple can be described by the equation:
V(t) = Vss(1 - e^(-t/τ))
Where:
- V(t) is the voltage at time t
- Vss is the steady-state voltage
- t is the time elapsed
- τ (tau) is the time constant
98% of Steady-State Value:
To find the time taken by the thermocouple to reach 98% of the steady-state value, we can substitute V(t) = 0.98Vss in the above equation:
0.98Vss = Vss(1 - e^(-t/τ))
Simplifying the equation, we get:
0.98 = 1 - e^(-t/τ)
e^(-t/τ) = 0.02
Taking the natural logarithm of both sides, we have:
-t/τ = ln(0.02)
t/τ = -ln(0.02)
t = -τ * ln(0.02)
Comparing Time Constant and Time Taken:
From the above equation, it is clear that the time taken by the thermocouple to reach 98% of the steady-state value is dependent on the time constant (τ). The time constant determines the rate at which the thermocouple responds to changes in temperature.
Since the time taken is proportional to the time constant (t = -τ * ln(0.02)), it can be concluded that the time taken is equal to four times the value of the time constant (t = 4τ).
Hence, the correct answer is option 'C' - equal to four times the value of the time constant of the thermocouple.
Time Constant:
The time constant of a thermocouple is a measure of how quickly it responds to changes in temperature. It is defined as the time it takes for the thermocouple to reach approximately 63.2% of its steady-state value when subjected to a step change in temperature.
Response of Thermocouple:
When a thermocouple is suddenly immersed in a medium of high temperature, it tends to reach a steady-state value over time. The response of the thermocouple can be represented by an exponential function.
Formula:
The response of a thermocouple can be described by the equation:
V(t) = Vss(1 - e^(-t/τ))
Where:
- V(t) is the voltage at time t
- Vss is the steady-state voltage
- t is the time elapsed
- τ (tau) is the time constant
98% of Steady-State Value:
To find the time taken by the thermocouple to reach 98% of the steady-state value, we can substitute V(t) = 0.98Vss in the above equation:
0.98Vss = Vss(1 - e^(-t/τ))
Simplifying the equation, we get:
0.98 = 1 - e^(-t/τ)
e^(-t/τ) = 0.02
Taking the natural logarithm of both sides, we have:
-t/τ = ln(0.02)
t/τ = -ln(0.02)
t = -τ * ln(0.02)
Comparing Time Constant and Time Taken:
From the above equation, it is clear that the time taken by the thermocouple to reach 98% of the steady-state value is dependent on the time constant (τ). The time constant determines the rate at which the thermocouple responds to changes in temperature.
Since the time taken is proportional to the time constant (t = -τ * ln(0.02)), it can be concluded that the time taken is equal to four times the value of the time constant (t = 4τ).
Hence, the correct answer is option 'C' - equal to four times the value of the time constant of the thermocouple.
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A thermocouple is suddenly immersed in a medium of high temperature. The approximatetime taken by the thermocouple to reach 98% of the steady-state value isa)equal to the time constant of the thermocoupleb)equal to twice the value of the time constant of the thermocouplec)equal to four times the value of the time constant of the thermocoupled)independent of the time constantCorrect answer is option 'C'. Can you explain this answer?
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A thermocouple is suddenly immersed in a medium of high temperature. The approximatetime taken by the thermocouple to reach 98% of the steady-state value isa)equal to the time constant of the thermocoupleb)equal to twice the value of the time constant of the thermocouplec)equal to four times the value of the time constant of the thermocoupled)independent of the time constantCorrect answer is option 'C'. 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 is suddenly immersed in a medium of high temperature. The approximatetime taken by the thermocouple to reach 98% of the steady-state value isa)equal to the time constant of the thermocoupleb)equal to twice the value of the time constant of the thermocouplec)equal to four times the value of the time constant of the thermocoupled)independent of the time constantCorrect answer is option 'C'. 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 is suddenly immersed in a medium of high temperature. The approximatetime taken by the thermocouple to reach 98% of the steady-state value isa)equal to the time constant of the thermocoupleb)equal to twice the value of the time constant of the thermocouplec)equal to four times the value of the time constant of the thermocoupled)independent of the time constantCorrect answer is option 'C'. Can you explain this answer?.
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