Question

A room in a house measures 3.2 m × 5.9 m × 4.8 m. Assuming no heat or material losses, how many grams of natural gas (methane, CH4) must be burned to heat the air in this room from 15.0oC to 25.0oC. Assume that air is 78% N2 and 22% O2, has a normal atmospheric pressure (1.01325 bar) and use data from Table 3-1 and Appendix D. The products of combustion are in the gas phase.

Answer 1

Heat of combustion of methane when products are all gases = - 802 KJ/mol

Average Heat capacity of air between 15 to 25 ⁰c and 1.01325 bar ( 78% N₂ + 22% O₂) = 1.00 KJ/Kg.K

Now,

Heat gained by the air, H = m₁s₁

Volume of the air = Volume of the room = 3.2*5.9*4.8 = 90.624 m³

Density of air at 15⁰C is 1.225 Kg/m³.

Mass = 90.624*1.225 = 111.0144 Kg

= 25-15 = 10 ^oc = 10 K.

H = 111.0144*1.00*10 = 1110.144 KJ

Now, heat released by 1 mole ( 16 g ) Methane gas = -802 KJ

Hence, mass of methane must be burn to release 1100.144 KJ heat = 16*1110.144/802 = 22.14 g.