Question

We burn fuels to extract heat. Some of the energy in the fuel is lost for practical purposes since it goes to the atmosphere with the hot combustion gases. The temperature that the combustion gases would attain if we did not extract any heat (Q=0) from the system is called the adiabatic flame temperature (Sometimes called Theoretical Flame Temperature, TFT). Find the adiabatic flame temperature for the combustion of CO with 100% excess air, if CO and dry air come into the combustor at 100 °C. H o f, CO = -110.52 kJ/mol H o f, CO2 = -393.51 kJ/mol Cp, gas = 30 J/mol.°C

Answer 1

All the CO is consumed to form CO2, this is the limiting reactant.

The excess air is a non reacting component, but requires sensible heat to raise its temperature to the adiabatic reaction temperature

The reaction ocurring is as follows

The first thing to consider is a basis in this case let´s consider a basis of 1 mol of CO and a initial temperature of 25C.

Now the air composition is 21% O₂ and 79% N₂

So let´s analize the material balance.

For the sthoichometry we know that we require 0.5 moles of each mole of CO. We are putting an air excess of 100% that means we have the double ammount of moles that we need (1 mole of O₂ ).

To get the quantity of nitrogen, we have to calcule the total ammount of air we have:

so we divide

The quantity of Nitrogen is 4.76 moles of all the air multyplied by 0.79 = 3.76 moles

Summarizing the material balance we have:

Component in                                                 Component out

CO                    1 mol                                                       0 mol

O₂ (needed + xs)    1 mol                                                     0.5 moles

N₂             3.76 moles                                               3.76 moles

Now we have to make the energy balance for each specie:

To do this we need the values of Cp of CO, CO2, N2 and O2 or the enthalpy values from book

and formation enthalpy of CO2 and CO.

We have the Cp of CO and the formation enthalpies.

The point here is to find a point where Q = 0 which means that the change of enthalpy is equal to zero.

So we have to find a temperature that will make the enthalpy change equal to zero.

Also the enthalpies for CO and CO2

I´m taking enthalpy values of combustion gases from a book of energy balance I´m taking those from 2000 K and 1750 K

Change of Enthalpy at 2000 K is 36740 J

Change of Enthalpy at 1750 K is -16657 J

The Temperature is between 1750 K and 2000 K. We are looking for a temperature where the change of enthalpy is zero.

Let´s interpolate between these 2 points with the next equation:

For our case will be like:

T flame = 1828 K

in Celsius = 1828 - 273 = 1555 C

Note: You can use the Cp formula for each specie

Cp= a + bT + CT² + dT³

You can find the values of a, b, c and d on a book or internet but be careful with the range of temperature those values are valid