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

To solve the problem, we need to find the rate of supply of butane (C₄H₁₀) and oxygen (O₂) that will produce the same calorific output as the given rate of methane (CH₄) and its corresponding oxygen supply.

### Step-by-Step Solution:

1. **Understanding the Heat of Combustion:**
- The heat of combustion for methane (CH₄) is given as \( 809 \, \text{kJ/mol} \).
- The heat of combustion for butane (C₄H₁₀) is given as \( 2878 \, \text{kJ/mol} \).

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