Q \#1 (30 Points) A steam heated stirred tank shown in Figure 2.3 of your text book has the following operating conditions and constant parameters: T=40CLatentheatofvaporization(Hv)ofwater=600calsgC=1calswi=104kgh=103kgm3v=100m3 The manipulated variable (MV) is the steam rate and the controlled variable (CV) is the tank temperature. The set point of the CV is 150C. Assume the inlet temperature Ti stays constant for the operations below. (a) (5 pts) What is the steady state steam flow rate at the set point temperature? (b) (5 pts) Assuming a linear dynamic model in terms of deviation variables, what are the values of the process gain and the time constant (include units)? (c) (10 pts) Suppose the steam is operating at the steady state steam flow rate calculated in (a). If the steam rate is then halved, what will be the new steady state temperature? How long does it take to reach within a 1C of the final steady state? (d) (10 pts) How can the time to reach the yalue in (c) be shortened? Suppose the steam rate is set to zero; how long does it take to reach T=95C ? Will the temperature remain at 95C once it reaches the new steady state