If a natural gas heater supplies 6.4 x 10^6 J of energy with an 75.2 % heat transfer efficiency, how many grams of methane must be burned? (He = -803 kJ/mol)

Answer 1

If the heater supplies 6.4 x 10⁶ J at 75.2% efficiency, the methane must supply 6.4 x 10⁶ J / 0.752 = 8.5 x 10⁶ J or equivalently 8.5 10³ kJ.

Since the combustion of CH4 produces 803 kJ /mole, the number of moles needed is 8.5 x 10³ kJ / 803 kJ/mole or 10.6 mols CH4.