The transfer function, which is the first-order dynamics of a heater of a semiconductor core, shows the relationship between the power level P at the heater input and the changes in temperature T is given below. T'(s) / P'(s) = K / (τs+1) Here the unit of K is 0C/Kw and the unit of τ is min. When an engineer changed the power input in steps from 1 to 1.5 kW, the process was steady. The engineer notes the following; (i) Process temperature is initially 80 0C. (ii) 4 minutes after the change of power input, the temperature is 120 0C. (iii) It is 280 0C after 30 minutes. (a) What are K and τ in the process transfer function? (b) Another time, what will be the maximum rate of change of process temperature if the engineer linearly changes the power input at a rate of 0.5 kW/min?

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