Question

A temperature-sensitive transducer is subjected to sudden temperature change. It takes 10 s for the transducer to reach equilibrium condition (five time constants). How long will it take for the transducer to read half of the temperature difference?

• A. 0.139 sec
• B. 13.9 sec
• C. 1.39 sec
• D. 139 sec

Answer 1

The correct option is C 1.39 sec

Time to reach equilibrium conditions

$=5\tau =10s$.

$\therefore Timeconstant\tau =10/5=2s.$

Now we have,

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

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

The time to read half of the temperature difference can be calculated as under:

$0.5=1-\left[exp\right(-t/2\left)\right]$

$ort=1.39s.$

$\therefore$ Time to read half of the temperature different is 1.39 s.