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A closed room of capacity 5 mx 5 mx 3 m can be heated by a furnace. The furnace may be either off or on. When the furnace is on, the heating supplied by the furnace is 1.5 x 108 cal/h. The heat capacity of air in the room is 0.17 cal/g-C, and density is 1190 g/m. The overall heat transfer coefficient for the room UA = 45000 cal/h-C. The outside air temperature is 10 C. The initial temperature in the room is 20 C. a. Sketch the system, and set up heat balance for temperature change in the room b. Set up the transfer function relating temperature in the room to heat supplied by the furnace, and to the outside air temperature C. Calculate the time constant and process gain parameters (Ans: t = 0.34 h)