Chapter 1, Problem 27P

A $\text{5-m}\times \text{ 6-m }\times \text{8-m}$ room is to be heated by an electrical resistance heater placed in a short duct in the room. Initially, the room is at ${15}^{\circ }\text{C,}$ and the local atmospheric pressure is 98 kPa. The room is losing heat steadily to the outside at a rate of 200 kJ/min. A 300-W fan circulates the air steadily through the duct and the electric heater at an average mass flow rate of 50 kg/min. The duct can be assumed to be adiabatic, and there is no air leaking in or out of the room. If it takes 18 min for the room air to reach an average temperature of ${25}^{\circ }\text{C,}$ 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.