In order to achieve maximum calorific output and clean flame characteristics, an industrial gas burn

Question

In order to achieve maximum calorific output and clean flame characteristics, an industrial gas burner must be supplied with an optimum fuel-to-oxygen ratio that corresponds to precisely $3.0$ times the theoretical oxygen requirement for complete combustion of the fuel. A burner originally calibrated and adjusted for methane ($	ext{CH}_4$) as fuel operates at a methane supply rate of $x	ext{ L hr}^{-1}$ and an oxygen supply rate of $6x	ext{ L hr}^{-1}$. This burner is now to be readjusted to burn gaseous butane ($	ext{C}_4	ext{H}_{10}$) instead of methane. Assume that all gases behave ideally under identical temperature and pressure conditions, and that efficiency losses due to incomplete combustion remain identical for both fuels. The standard molar heats of combustion are: $\Delta H^\circ_c[	ext{CH}_4(g)] = -809	ext{ kJ mol}^{-1}$ and $\Delta H^\circ_c[	ext{C}_4	ext{H}_{10}(g)] = -2878	ext{ kJ mol}^{-1}$.

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