Problem 5 A heater for a semiconductor wafer has first-order dynamics, that is, the transfer function relating changes in temperature TC to changes in the heater input power level PkW is P(s)T(s)=s+1K where K is the gain and is the time constant of the heater system in minutes. The process was at steady state when an engineer changed the power input stepwise from 1kW to 3kW. The engineer noticed the following: (i) The process temperature was initially at 50C. (ii) Five minutes after changing the power input, the temperature is 55C. (iii)Twelve minutes later the temperature is 58C. Determine the values of the gain (K) and time constant () in the heater transfer function