1.) A mercury-in-glass thermometer initially at 30 degree Celsius is suddenly im

Question

1.) A mercury-in-glass thermometer initially at 30 degree Celsius is suddenly immersed into a liquid that is maintained at 120 degree Celsius. After a time interval of 2.0 sec, the thermometer reads 80 degree Celsius. Assuming a first-order system, estimate the time constant of the thermometer.

2.) A pressure transducer behaves as a second-order system. If the undamped natural frequency is 10 Khz and the damping is 85% of the critical, determine the frequency range(s) over which the measurement error is not greater than
a. 10%.
b. 20%.

Explanation / Answer

a) Rate = k * T where T= temperature and k= inverse of time constant

dT/dt = k*T

integrating , ln(T1/T2) = k(t1-t2) where t = time,

ln(30/80) =k* (0-2)

solving we get k= 0.49 sec-1

Time constant = 1/k = 2.0391 sec

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