Methane combusts with air in a furnace as $\mathrm{CH}_{4}+2 \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}$. The heat of reaction $\Delta H_{r x n}=-880 \mathrm{~kJ}$ per mol $\mathrm{CH}_{4}$ 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 $44 \mathrm{~J} \mathrm{~mol}^{-1}{ }^{\circ} \mathrm{C}^{-1}$. Air may be considered as $20 \mathrm{~mol} \% \mathrm{O}_{2}$ and $80 \mathrm{~mol} \% \mathrm{~N}_{2}$. The air-fuel mixture enters the furnace at $50^{\circ} \mathrm{C}$. The methane conversion $X$ varies with the air-to-methane mole ratio, $r$, as
\[
X=1-0.1 e^{-2\left(r-r_{s}\right)} \quad \text { with } \quad 0.9 r_{s} \leq r \leq 1.1 r_{s}
\]
where $r_{s}$ is the stoichiometric air-to-methane mole ratio. For $r=1.05 r_{s}$, the exit flue gas temperature in ${ }^{\circ} \mathrm{C}$, rounded off to $1$ decimal place, is $\_\_\_\_\_\_\_\_$