Question

A temperature probe having a first order response with a time constant of 1 sec is given a step input of 50°C from 0°C. The correct plot of temperature characteristics is

• A.
• B.
• C.
• D. none of these

Answer 1

The correct option is A

$\text{Given data}:\tau =1sec=\text{time constant}{\theta }_{initial}=0^{\circ }C=\text{Initial temeprature}{\theta }_{final}={50}^{\circ }C=\text{final temperature}$

$\theta \left(t\right)={\theta }_{final}+({\theta }_{initial}-{\theta }_{final})e^{-t/\tau }$

$\theta \left(t\right)=50+(0-50)e^{-t}$

$att=0.4sec\theta (t=0.4)={16.48}^{\circ }C$

$att=0.8sec\theta (t=0.8)={27.53}^{\circ }C$

$att=1.0sec\theta (t=1)={31.61}^{\circ }C$

from this data we can say option (a) is the only right choice.