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# Methane gas $(CH_4)$ at $25^\circ C,$ 1 atm and a volumetric flow rate of $27 m^3/h$ enters a heat-treating furnace operating at steady state. The methane burns completely with 140% of theoretical air entering at $127^\circ C,$ 1 atm. Products of combustion exit at $427^\circ C,$ 1 atm. Determine a. the volumetric flow rate of the air, in $m^3/h.$ b. the rate of heat transfer from the furnace, in kJ/h.

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Write the balanced chemical equation of $CH_4$ for complete combustion with theoretical amount of dry air,

$CH_4+ 2(O_2+3.76N_2)\rightarrow CO_2+2 H_2O+7.52 N_2$

( $\therefore$ 3.76 moles of $N_2$ accompany each mole of $O_2$ in the air)

Now write the balanced chemical equation of $CH_4$ for combustion with 140 $\%$ of theoretical amount of dry air

$CH_4+ 2(1.4)(O_2+3.76N_2)\rightarrow CO_2+2 H_2O+0.8N_2+10.528 N_2$

$CH_4+ 2.8(O_2+3.76N_2)\rightarrow CO_2+2 H_2O+0.8N_2+10.528 N_2$

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