Friday, February 17, 2006

Room Heating

Power Requirements

Q) A heater is used to keep a room at 20oC. Every half hour the air in the 62m3 is swapped for new air at 5oC (in reality this swap happens smoothly over the course of the half hour so the temperature remains stable). Additionally, heat is lost through the walls of the room at a rate of 850kJ/hour.

What is the minimum power required of the heater?

A) We can calculate the heat energy required to keep the room hot over the course of an hour: There are two separate heating requirements – heating the new air and replacing the heat lost.

1) 5o -> 20o in 30mins

62m3 of air has a mass of 81kg (ρair=1.3 kg/m3)

The heat energy required to heat the air is: 206.55 kcal over the course of half an hour.




2) The rate of heat loss through the walls:



the total power requirements for heating
    P = Pair + Pwalls

    P = 1.5kW

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