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Instrumentation & Process Control
Measurement Instruments
GATE 2012
Medium

A thermometer initially at 100°C is dipped at t=0 into an oil bath, maintained at 150°C. If the recorded temperature is 130°C after 1 minute, then the time constant of thermometer (in min) is

  • A1.98
  • B1.35
  • C1.26
  • 1.09

Explanation

First order step response: (T−Tbath)/(T0−Tbath)=e^(−t/τ). (130−150)/(100−150)=(−20)/(−50)=0.4=e^(−1/τ) ⟹ τ=−1/ln(0.4)=1/0.9163≈1.09 min.

Source: GATE CH 2012 (2012)

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