An electrically heated stirred tank system of section 2.4.3 (page 23) of the Textbook is modeled by the following second

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An electrically heated stirred tank system of section 2.4.3
(page 23) of the Textbook is modeled by the following second order
differential equation: 9 d 2T/dt 2 + 12 dT/dt + T = T i + 0.05 Q
where T i and T are inlet and outlet temperatures of the liquid
streams and Q is the heat input rate. At steady state T i,ss = 100
oC, T ss = 350 oC, Q ss=5000 kcal/min (a) Obtain the transfer
function T’(s)/Q’(s) for this process (b) Time constant τ and
damping coefficient ζ in the transfer function are: (c) At t=
0, if Q is suddenly changed from 5000 kcal/min to 6000 kcal/min,
calculate the exit temperature T after 2 minutes. (d) Calculate the
exit temperature T after 8 minutes.