Combustion of natural gas (primarily methane) occurs in most household heaters.
ID: 894677 • 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 × 25.0 m × 3.0 m ; specific heat capacity of air is 30 J/Kmol; 1.00 mol of air occupies 22.4Lfor all temperatures concerned.
Explanation / Answer
total volume of house = 30*25*3 = 2250 m^3
= 2250*10^3 L = 2.25*10^6 L ( 1 m^3 = 10^3 L)
No of mole of air present in house = 2.25*10^6/22.4
= 100446.43 mole
amount of heat gained by air qair = n*S*DT
n = No of mole of air present in house = 100446.43 mole
S = specific heat capacity of air = 30 J/Kmol
DT = 15 C
qair = 100446.43*30*15 = 45200893.5 joule
= 45200.0 kj
enthalpy of combustion of CH4 = - -803 kj/mol
so that
NO of moles of CH4 burned = 45200.0/803 = 56.3 mole
mass of CH4 burned = 5.63*16 = 900.8 grams