The adiabatic flame temperature is that temperature reached when all of the sensible heat released by the combustion of a fuel is used to raise the temperature of the gaseous products of combustion. Consider the adiabatic flame temperature reached when acetylene, C2H2, is combusted at 298 K with

Question

The adiabatic flame temperature is that temperature reached when all of the sensible heat released by the combustion of a fuel is used to raise the temperature of the gaseous products of combustion. Consider the adiabatic flame temperature reached when acetylene, $C_2H_2$ , is combusted at 298 K with (1) the stoichiometric amount of oxygen and (2) the number of moles of air containing the stoichiometric number of moles of oxygen. Air is, by mole or volume percent, 21% $O_2$ and 79% $N_2$ .

The combustion reaction with stoichiometric oxygen is

$C_2H_2+2.5 O_2=2 CO_2+H_2O$ (i)

For $C_2H_2: \Delta H_{298}=+226,700$ J

For $CO_2: \Delta H_{298}=-393,500$ J

For $H_2O: \Delta H_{298}=-241,800$ J

The combustion reaction with stoichiometric oxygen is

[latex]C_2H_2+2.5 O_2=2 CO_2+H_2O[/latex] (i)

For [latex]C_2H_2: \Delta H_{298}=+226,700 [/latex] J

For [latex]CO_2: \Delta H_{298}=-393,500[/latex] J

For [latex]H_2O: \Delta H_{298}=-241,800[/latex] J

Accepted Answer

Thus, for the reaction given by Equation (i):

[latex]\Delta H_{(i)_{298} }=(-2 imes 393,500)-241,800-226,700=-1,255,500 [/latex] J

The constant-pressure molar heat capacities of the products of reaction are

For [latex]H_2O: c_{p},H_2O =30.00+10.71 imes 10^{-3} T+0.33 imes 10^{5}T^2[/latex] J/K.mole

For [latex]CO_2: c_{p},CO_2 =44.14+9.04 imes 10^{-3} T-8.54 imes 10^{5}T^2[/latex] J/K.mole

The adiabatic flame temperature, T , is then obtained from the requirement

[latex]\Delta H_{(i)_{298} }+\int_{298}^{T}{(2c_p,CO_2+c_p,H_2O)}dT=0 [/latex]

or

[latex]-1,255,500+118.28 imes (T-298)+14.40 imes 10^{-3} imes (T^2-298^2) [/latex]

[latex]+16.75 imes 10^5(1/T-1/298) =0[/latex]

which has the solution [latex]T=6,236[/latex] K.

For combustion with the stoichiometric amount of air, the reaction is written as

[latex]C_2H_2+2.5 O_2+2.5 imes (79/21)N_2=2CO_2+H_2O+9.41N_2[/latex]

For [latex]N_2: c_p,N_2=27.87+4.27 imes 10^{-3}T [/latex] J/mole.K

and the adiabatic flame temperature, T , is obtained from

[latex]\Delta H_{(i)_{298} }+\int_{298}^{T}{(2c_p,CO_2+c_p,H_2O+9.41c_p,N_2)}dT=0 [/latex]

or

[latex]-1,255,500+380.1 imes (T-298)+40.16 imes 10^{-3} imes (T^2-298^2) [/latex]

[latex]+16.75 imes 10^5(1/T-1/298)=0 [/latex]

as [latex]T=2,797 [/latex] K

This high adiabatic flame temperature facilitates the use of acetylene for welding metals with high melting temperatures.

Question 6.11.3: The adiabatic flame temperature is that temperature reached ...

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