Example 5.1 derives the gain and time constant for a first-order model of a stirred tank heating process. 

(a) Simulate the response of the tank temperature to a step change in heat input from 3×10⁷ cal/h to 5×10⁷ cal/h.

(b) Suppose there are dynamics associated with changing the heat input to the system. If the dynamics of the heater itself can be expressed by a first order transfer function with a gain of one and a time constant of 10 min, what is the overall transfer function for the heating system (tank plus heater)?
(c) For the process in (b), simulate the step increase in heat input.