GATE 2026 MT – Question 61
For the reaction between methane and stoichiometric air containing 20 vol.% $\mathrm{O_2}$ and 80 vol.% $\mathrm{N_2}$, the estimated adiabatic flame temperature is ________ K. (Rounded off to one decimal place.)
$\mathrm{CH_4(g)+2O_2(g)\to CO_2(g)+2H_2O(g)}$.
Given $\Delta H=-850\ \mathrm{kJ/mol}$ at 298 K. Assume a constant molar heat capacity $C_p=50\ \mathrm{J/(mol\,K)}$ for each reactant and product.
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Correct answer: 1842.5 to 1844.5
Explanation
One mole of methane needs 2 moles of oxygen. The given air composition brings $2(80/20)=8$ moles of nitrogen, so the products contain $1+2+8=11$ moles.
Assuming reactants enter at the 298 K reference temperature, the adiabatic balance is $850000=11(50)(T_f-298)$. Thus $T_f=298+850000/550=1843.4545\ \mathrm K$, giving **1843.5 K**. The initial reactant temperature is implicit in this intended calculation.