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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 25C150C, then the temperature indicated by the device after the 10 sec of process has been started is _________ C.

A
140.58
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B
128.64
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C
150
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D
133.08
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Solution

The correct option is D 133.08
Final steady state temperature

θF=150C

Initial temperature

θi=25C

Time constant τ=5s

Therefore, the temperature after 10 sec is given by

θ=θF+(θiθF)[exp(tτ)]

=150+(25150)[exp(105)]

=133.08C

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