A building with an internal volume of 400 m3 is to be heated by a 30 - kW electric resistance heater placed in the duct inside the building. Initially, the air in the building is at 14°C, and the local atmospheric pressure is 95 kPa. The building is losing heat to the surroundings at a steady rate of 450 kJ/min. Air is forced to flow through the duct and the heater steadily by a 250-W fan, and it experiences a temperature rise of 5°C each time it passes through the duct, which may be assumed to be adiabatic.
(a) How long will it take for the air inside the building to reach an average temperature of 24°C?
(b) Determine the average mass flow rate of air through the duct.

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450 kJ/min T2= T1+ 5°C P=95kPa We,in = 30 kW 14°C → 24°C m Ti 250 W FIGURE P5-188