How Much Heat is Needed to Raise the Temperature of a House?

[Gonger]

I have a question I'm trying to but I don't really know where to start. It is kind of an add-on to a previous question that I got pretty easliy. This is the first question:

A house has well-insulated walls (assume same thermal conductivity as air, 0.023 W/(m·K)) 16.2 cm thick, with an area of 415 m2, a roof of wood (conductivity 0.10 W/(m·K)) 7.0 cm thick, with an area of 290 m2, and plain glass (conductivity 0.84 W/(m·K)) windows 0.60 cm thick, with an area of 31.7 m2. Assuming that the heat loss is only by conduction, calculate the rate at which heat must be supplied to this house to maintain its temperature at 20.1 °C if the outside temperature is -11.7 °C.

The answer to that was 156000 W. Now the second question asks how much heat must be supplied to raise the temperature and this is what I don't know how to do. This is the second question:

If the house is initially at 13.8 °C, calculate how much heat must be supplied to raise the temperature to 20.1 °C within 29.0 min. Assume that only the air (specific heat 1004 J/(kg·K), density 1.29 kg/m3) needs to be heated and that its volume is 750 m3.

If anybody has any help for me that would be great. Thanks

 

[Nenad]

use your same approach as in question 1. Find out the amount of heat lost in the heating process, and then find out the amount of heat needed to raise the temp the air in that volume. Then use q=mct, and fool around with the equations. You should be able to get it.

Regards,

Nenad

 

[Gonger]

the thing I don't know how to do is find out how to calculate the heat needed to raise the temperature

 

[Nenad]

use:
$$q = mc \Delta t$$

you need to find out what c is for air, and what the mass of air you have in that volume. For this you need to know the mass per unit volume of air. Once you find these out (data tables), you can solve for q. Then once you hve q, you have the amount of heat needed to rise the temperture, but you need to remember that there is also heat loss through insulation.

Regards,

Nenad