In order to get maximum calorific output a burner should have an optimum fuel to oxygen ratio which corresponds to three times as much oxygen as is required theorectically for complete combusion of the fuel A burner which has been adjused for methane as fuel (with `x L h^(-1)` of `CH_(4)` and `6x Lh^(-1) of CO_(2))` is to be readjusted for butane `C_(4)H_(10)` in order to get the same calorific output what should be the rate of supply to butane and oxygen? Assume that losses due to incomplete combustion etc are the same for both fuels and that the gases behave ideally Heats of combusion
`CH_(4) =809 kJ mol^(-1),C_(4)H_(10) =2878 kJmol^(-1)` .

Explanation

`{:(,CH_(4), +2O_(2)to,CO_(2)+,2H_(2)O),("Initial volume/hr",x,6x,x,6x):}`
`DeltaH = -809 kJ "mol"^(-1)`
Let, the temperature be T and assume volume of 1 mole of a gas is V litre at this condition.
`therefore` V litre of 1 mole `CH_(4)` gives energy on combustion = 809 kJ
x litre of `CH_(4)` gives energy on combustion `=(809 (x))/V kJ`
`therefore 2878` kJ energy is obtained by 1 mole or V litre `C C_(4)H_(10)`
`therefore (809 (x))/V kJ` energy is obtained by `=(809 (x) xx V)/(V xx 2878) L C_(4)H_(10)`
`=0.281 (x) L C_(4)H_(10)`
Thus butane supplied for same colorific output `=0.281 xx L`
`therefore C_(4)H_(10) + 13/2 O_(2) to 4CO_(2) + 5H_(2)O, DeltaH = -2878` kJ/mole.
Volume of `O_(2)` required = `3 xx "Volume of" O_(2) "for combustion of" C_(4)H_(10)`
`=3 xx 13/2 xx "Volume of" C_(4)H_(10) = 3 xx 13/2 xx 0.281 (x) = 5.48 (x) L O_(2)`