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Assume that an ordinary mercury-in-glass thermometer follows first order dynamics with a
time constant of 10s. It is at a steady state temperature of 0°C. At time t = 0, the thermometer
is suddenly immersed in a constant temperature bath at 100°C. The time required (in s) for
the thermometer to read 95°C, approximately is
  • a)
    60
  • b)
    40
  • c)
    30
  • d)
    20
Correct answer is option 'C'. Can you explain this answer?
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Assume that an ordinary mercury-in-glass thermometer follows first ord...
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Assume that an ordinary mercury-in-glass thermometer follows first ord...
°C, but suddenly the temperature is increased to 50°C. How long will it take for the thermometer to reach 90% of the final temperature?

We can use the formula for first order dynamics:

T(t) = Tfinal - (Tfinal - T0)e^(-t/τ)

where T(t) is the temperature at time t, Tfinal is the final temperature, T0 is the initial temperature (steady state temperature in this case), τ is the time constant, and e is the base of the natural logarithm.

We know that T0 = 0°C, Tfinal = 50°C, and τ = 10s. We want to find the time it takes for the temperature to reach 90% of the final temperature, which means T(t)/Tfinal = 0.9.

0.9 = 1 - e^(-t/τ)

Taking the natural logarithm of both sides:

ln(0.1) = -t/τ

Solving for t:

t = -ln(0.1) * τ

t = -(-2.303) * 10s

t = 23.03s

Therefore, it will take approximately 23 seconds for the thermometer to reach 90% of the final temperature of 50°C.
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Assume that an ordinary mercury-in-glass thermometer follows first order dynamics with atime constant of 10s. It is at a steady state temperature of 0°C. At time t = 0, the thermometeris suddenly immersed in a constant temperature bath at 100°C. The time required (in s) forthe thermometer to read 95°C, approximately isa)60b)40c)30d)20Correct answer is option 'C'. Can you explain this answer?
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Assume that an ordinary mercury-in-glass thermometer follows first order dynamics with atime constant of 10s. It is at a steady state temperature of 0°C. At time t = 0, the thermometeris suddenly immersed in a constant temperature bath at 100°C. The time required (in s) forthe thermometer to read 95°C, approximately isa)60b)40c)30d)20Correct 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 Assume that an ordinary mercury-in-glass thermometer follows first order dynamics with atime constant of 10s. It is at a steady state temperature of 0°C. At time t = 0, the thermometeris suddenly immersed in a constant temperature bath at 100°C. The time required (in s) forthe thermometer to read 95°C, approximately isa)60b)40c)30d)20Correct 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 Assume that an ordinary mercury-in-glass thermometer follows first order dynamics with atime constant of 10s. It is at a steady state temperature of 0°C. At time t = 0, the thermometeris suddenly immersed in a constant temperature bath at 100°C. The time required (in s) forthe thermometer to read 95°C, approximately isa)60b)40c)30d)20Correct answer is option 'C'. Can you explain this answer?.
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