Question

A temerature sensing device can be modelled as a first order system with a time constant of 5 sec. If it is suddenly subjected to a step input of ${25}^{\circ }C-{150}^{\circ }C$, then the temperature indicated by the device after the 10 sec of process has been started is _________ ${}^{\circ }C.$

• A. 140.58
• B. 128.64
• C. 150
• D. 133.08

Answer 1

The correct option is D 133.08

Final steady state temperature

${\theta }_F={150}^{\circ }C$

Initial temperature

${\theta }_i={25}^{\circ }C$

Time constant $\tau =5s$

Therefore, the temperature after 10 sec is given by

$\theta ={\theta }_F+({\theta }_i-{\theta }_F)\left[exp\left(\frac{-t}{\tau }\right)\right]$

$=150+(25-150)\left[exp\left(\frac{-10}{5}\right)\right]$

$={133.08}^{\circ }C$