How Many Grams of Methane to Heat Your Home?

[hola]

Suppose you want to heat the air in your house with natural gas (CH_4). Assume your house has 275 m^2 of floor are and ceilings are 2.5 m from floors. The air in your house has a specific heat capacity of 29.1 J/mol K. The number of moles in the house can be found by assuming the molar mass of air is 28.9 g/mol and that the density of the air at these temperatures is about 1.22 g/L. How much grams methane do you have to burn to heat air from 15.0 to 22.0 C?

So, here is how I think I can solve it.
1. Determine number of moles of air. I have no idea how to do that.
2. specific heat*temp*moles of CH4 = specific heat*temp*moles of water.

But I can't! Any help, please?

 

[Ouabache]

For (1) you have been given all the information except volume conversion
1 cubic meter = 1000L

 

[hola]

Okay:
For air, I got:
Change in temp: 7.0 C
specific heat: 29.1 J/molK
mass= 839*10^5 g (should I convert this into moles?)
For methane:
specific heat: 4.18 j/molK
I need to solve for mass, right?
But I don't have temperature change in methane?

HELP! please, ?

 

[Pengwuino]

Well for one... how do you heat a house with methane without combustion?

You're missing a piece of information

 

[GCT]

2. specific heat*temp*moles of CH4 = specific heat*temp*moles of water.

why water?

First, how would you find the heat energy given off by the combustion of methane?