Room Heating

Power Requirements

Q) A heater is used to keep a room at 20^oC. Every half hour the air in the 62m³ is swapped for new air at 5^oC (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) 5^o -> 20^o in 30mins

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

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

P_air=.1148kcal/sec

P_air=.5kJ/s

P_air=.5kW

2) The rate of heat loss through the walls:

P_walls=850kcal/hr

P_walls=1kJ/s

the total power requirements for heating

P = P_air + P_walls

P = 1.5kW