Question

A temperture sensing device can be modelled as a first order system with a time constant of 6 s. It is suddenly subjected to a step input of ${25}^{o}C-{150}^{o}C$. What temperature will be indicated in 10s after the process has started?

• A. ${1264}^{o}C$
• B. ${1.264}^{o}C$
• C. ${12.64}^{o}C$
• D. ${126.4}^{o}C$

Answer 1

The correct option is D ${126.4}^{o}C$

It is given that ;

$\text{Final steady state temperature}{\theta }_0={150}^{o}C\text{,}$

$\text{Initial temperature}{\theta }_i={25}^{o}C,$

$\text{and time constant}\tau =6s$

Therefore, the temperature after 10 s can be calculated as,

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

$=150+(25-100)\left[exp\right(-10/6\left)\right]={126.4}^{o}C$