Express your answer in terms of W/m2.

Question

What is the average power per m2 of floor space for a 100 m2 apartment with a leakiness (heat-loss coefficient) of 9 kWh per day per oC and an average inside/outside temperature difference of 15oC. You may assume a heating/cooling system operating at 100% efficiency.

Answer 1

Hi John,  

 

The power loss for the apartment is PL = (9kWh/d/°C)×(15°C) = 135 kWh/d .  If the area of the apartment is A = 100 m²,  then PL/A = 1.35kWh/d/m² .  Now we need to "massage" (multiply) this answer with some units conversion factors; namely 1000 W/kW and 1day/24h.  Thus PL/A = (1.35)(1000)(1/24) kWh/d/m²)(W/kW)(d/h) = 56.25 W/m²  (taking some care to correctly cancel units).

Answer 2

If you lose 9 kWh         , and inside - outside temperature difference = 15 oC, then for a 100 m^2 floor,

                day -oC

 

Q = (9 kWh/day/oC) * (15 oC) / (100 m^2)

 

Q = 1.35 kWh/day/m^2 * (1000 W/kW) * (1 day/24 hrs)

 

Q = 56.25 W/m^2 of heat loss each day to maintain 15 oC difference between the inside and outside temperature

 

 

If the heating/cooling efficiency is 100%, then this represents the amount of energy that must be supplied to the room.

 

If the system efficiency were lower, then you would divide your answer by that efficiency (in decimal form).  Therefore, more energy needs to be added to the room, due to inefficiencies.