Question

Methane combusts with air in a furnace as $CH₄ + 2O₂$ → $CO₂ + 2H₂O.$ The heat of reaction $\Delta H_{rxn} = −880$ kJ per mol $CH₄$ and is assumed constant. The furnace is well-insulated and no other side reactions occur. All components behave as ideal gases with a constant molar heat capacity of $44 J/(mol\cdot °C).$ Air is 20 mol% $O₂$ and 80 mol% $N₂.$ The air-fuel mixture enters the furnace at $50°C.$ The methane conversion X varies with the air-to-methane mole ratio, r, as X $= 1 − 0.1e^{−2(r−rs)}$ with 0.9rs $\leq$ r $\leq$ 1.1rs, where rs is the stoichiometric air-to-methane mole ratio. For r = 1.05rs, the exit flue gas temperature in $°C,$ rounded off to 1 decimal place, is ______

Official answer: 1719 to 1730