GATE 2024 CH – Question 55

Methane combusts with air in a furnace as $CH_4 + 2O_2 \to CO_2 + 2H_2O$. The heat of reaction $\Delta H_{rxn} = -880$ kJ per mol $CH_4$ and is assumed to be 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$^{-1}$ °C$^{-1}$. Air may be considered as 20 mol% $O_2$ and 80 mol% $N_2$. The air-fuel mixture enters the furnace at 50 °C. The methane conversion $X$ varies with the air-to-methane mole ratio, $r$, as $X = 1 - 0.1e^{-2(r - r_s)}$ with $0.9r_s \le r \le 1.1r_s$ where $r_s$ is the stoichiometric air-to-methane mole ratio. For $r = 1.05r_s$, the exit flue gas temperature in °C, rounded off to 1 decimal place, is ______