Methane combusts with air in a furnace as \( \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \). The heat of reaction \( \Delta H_\text{r} = -880 \, \text{kJ/mol CH}_4 \), 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 \( c_p = 40 \, \text{J mol}^{-1} \, \text{°C}^{-1} \). Air may be considered as 20 mol\% \( \text{O}_2 \) and 80 mol\% \( \text{N}_2 \). The air-fuel mixture enters the furnace at \( 50 \, \text{°C} \). The methane conversion \( X \) varies with the air-to-methane mole ratio, \( r \), as:
\[
X = 1 - 0.1e^{-2(r-r_s)}, \, \text{with} \, 0.9r_s \leq r \leq 1.3r_s,
\]
where \( r_s \) is the stoichiometric air-to-methane mole ratio. For \( r = 1.05r_s \), the exit flue gas temperature in \( \, \text{°C} \), rounded off to 1 decimal place, is:
