A $5-m6-m8-m$ room is to be heated by an electric resistance heater placed in a short duct in the room. Initially, the room is at $15C,$ and the local atmospheric pressure is $98$ kPa $.$ The room is losing heat steadily to the outside at a rate of $200k\frac{J}{m}in.$ A $200-$W fan circulates the air steadily through the duct and the electric heater at an average mass flow rate of $50k\frac{g}{m}in.$ The duct can be assumed to be adiabatic, and there is no air leaking in or out of the room. If it takes $15$ min for the room air to reach an average temperature of $25C,$ find $($a$)$ the power rating of the electric heater and $($b$)$ the temperature rise that the air experiences each time it passes through the heater.