Project ForgeInstrumentation & Process Control
Measurement Instruments
GATE 2014
Medium
Assume that an ordinary mercury-in-glass thermometer follows first order dynamics with a time constant of 10 s. 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
- A60
- B40
- 30
- D20
Explanation
For a first-order step response, (T−T0)/(Tf−T0)=1−e^(−t/τ). 0.95=1−e^(−t/10) ⟹ e^(−t/10)=0.05 ⟹ t=10·ln(20)=10×2.996≈30 s.
Source: GATE CH 2014 (2014)
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