Question

A thermometer has a time constant of 3.5 s. It is quickly taken from a temperature $0^{o}C$ to a water bath having a temperature ${100}^{o}C.$ What temperature will be indicated after 1.5 s?

• A. ${86.34}^{o}C$
• B. ${100.88}^{o}C$
• C. ${34.86}^{o}C$
• D. ${43.86}^{o}C$

Answer 1

The correct option is C ${34.86}^{o}C$

From above it is clear that the thermometer is subjected to a step input of ${100}^{o}C.$

The output temperature after 1.5 s is given as :

$\theta ={\theta }_0[1-exp(1-t/\tau \left)\right]$

$=100[1-exp(-1.5/3.5\left)\right]={34.86}^{o}C$