Combustion of natural gas (primarily methane) occurs in most household heaters.
ID: 918038 • Letter: C
Question
Combustion of natural gas (primarily methane) occurs in most household heaters. The heat given off in this reaction is used to raise the temperature of the air in the house.
Assuming that all the energy given off in the reaction goes to heating up only the air in the house, determine the mass of methane required to heat the air in a house by 15.0 C. Assume each of the following: house dimensions are 30.0 m × 35.0 m × 2.8 m ; specific heat capacity of air is 30 J/Kmol; 1.00 mol of air occupies 22.4L for all temperatures concerned.
Explanation / Answer
dT = 15°C
Qair = m*Cp*dT
V = 30*35*2.8 = 2940 m3 = 2.940*10^6 Liters
n = V/Vn = (2.940*10^6)/(22.4) = 131250 mol of air
Qair = n*Cp*dT = 131250 *30*15 = 59062500 J = 59062.5 kJ
Qair = Qmethane
Qmethane = Hcombt*m
HcomCH4 = 55.50*10^3 kJ/kg
Then, substitute in
Qmethane = Hcombt*m
59062.5 kJ = 55.50*10^3 kJ/kg * m
m = 59062.5/(55.50*10^3) = 1.06418 kg of methane are required