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Q#1 Energy Balance Calculations GATE CH 2024 NAT +2 marks -0 marks

Methane combusts with air in a furnace as \(CH_4 + 2O_2 → CO_2 + 2H_2O\). The heat of reaction\(ΔH_{rxn}= –800 kJ/mol\) \(CH_4\) 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 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

\(\begin{align*} X = 1 - 0.1 e^{-2(r - r_s)} \quad \text{with} \quad 0.9 r_s \le r \le 1.1 r_s \end{align*}\)

Where \(r_s\) is the stoichiometric air-to-methane mole ratio. For \(r= 1.05 r_s\) the exit flue gas temperature in °C, rounded off to 1 decimal place, is _ _ _ _ _ _

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