[Miss1nik2]

The question is...

You want to heat your house with natural gas CH4. The house has 275 sq. m of the floor area and the height of 2.5 m (between the floor and the ceiling). The air has a specific molar heat capacity of 29.1 j/mol*K. The molar mass of air is 28.9 and a density of 1.22 g/L at these temperatures. How much methane do you have to use in order to heat air from 15 to 22 oC in your house?

The answer I found was 142.4 g, but I wasnt sure about it.

Thank you for any thing you can tell me.

[Borek]

Hard to tell without methane combustion heat.

[Jasmine]

Hi,

I have attempted this problem myself. 

This is as far as I got:

Need to calculate the VOLUME of air in the House:
Area X Height = Volume of air in Cubic Meters

275 Sq. Meters + 2.5 Meters = 687.5 Meters cubed

V = 687.5 M3 X (1,000L/1 M3) = 687,500 Liters of Air

To get Mass of air, must convert Liters to grams via Density Equation 1.22 grams/L.

687,500 L X (1.22 grams/1.0 L) = 838,750 grams of Air,

To get Moles of Air,

838,750 grams X (1 Mole/28.9 grams) = 29,022.5 Moles of House air

29,022.5 Moles air X (29.1 Joules/Mole oK)  X 7o K = 844,554.75 X 7 = 5,911.883.25 Joules or 5911.9 Kilojoules.

This is where I come to a stop.

Do you use the Specific Heat Formula (Specific Heat X Mass X Temp Change = Heat Energy) or do you use this formula with Molar Heat of Combustion? 
Can you interchange Molar Heats with this formula or not?
Also Molar Heat of Methane (CH4) is that 4.94 Kilojoules/Mole? I see different values for this in different places.

Thanks,