Thermodynamics Combustion to find the air/fuel ratio

[Perspex1.2]

Homework Statement

A solid fuel supplied to a furnace had the following composition by mass.
Carbon: 86%
Hydrogen: 5%
Oxygen:4%
Incombustibles: 5%

Dry volumetric analysis of the combustion products showed the flue gas contained 15%
and 1.5% of CO2 and CO respectively. The test on the ashes discharged from the furnace
found 0.01 kg of un-burnt carbon per kilogram of the fuel supplied to the furnace.

Determine the air/fuel ratio by mass.

ANSWER is 12.67 if this helps


2. The attempt at a solution

So firstly I write out the combustion equation:

(0.86/12)C + (0.05/2)H₂ + (0.06/32)O₂ + 0.05ASH + Y(0₂ + 3.76 N₂) = aCO₂ + bH₂0 + d0₂ + fN₂ + 0.05ASH

Firstly is the combustion equation correct?

When I equate the element atoms I have too many variables missing:

a=(0.86/12)
b=(0.05/2)
O: (0.06/32)×2 + 2Y = 2a + b + 2d
N: (3.76Y)×2 = 2f

How do I calculate the value of Y and what do I do with the 0.01 kg of un-burnt carbon?

I would very much appreciate any help with this question. Thank you.

 

[KataKoniK]

Hello,

To calculate the value of Y, you can use the information given in the dry volumetric analysis of the combustion products. Since the flue gas contains 15% CO2 and 1.5% CO, we can assume that the remaining 83.5% is N2. Therefore, we can set up the following equation:

0.835 = 3.76Y + 2d

You can solve for Y using this equation and then use it in the equations for O and N to solve for the other variables.

As for the 0.01 kg of un-burnt carbon, you can include it in the equation for carbon balance:

0.86 = a + 0.01

This will give you the value of a, which you can then use in the other equations to solve for the remaining variables.

I hope this helps! Let me know if you have any further questions.