11.6: Adiabatic Flame Temperature
With a few simple approximations, we can estimate the temperature of a flame formed in a flowing gas mixture of oxygen or air and a fuel. We treat a moving segment of the gas mixture as a closed system in which the temperature increases as combustion takes place. We assume that the reaction occurs at a constant pressure equal to the standard pressure, and that the process is adiabatic and the gas is an ideal-gas mixture.
The principle of the calculation is similar to that used for a constant-pressure calorimeter as explained by the paths shown in Fig. 11.11. When the combustion reaction in the segment of gas reaches reaction equilibrium, the advancement has changed by \(\Del\xi\) and the temperature has increased from \(T_1\) to \(T_2\). Because the reaction is assumed to be adiabatic at constant pressure, \(\Del H\expt\) is zero. Therefore, the sum of \(\Del H(\tx{rxn},T_1)\) and \(\Del H(\tx{P})\) is zero, and we can write \begin{equation} \Del\xi\Delsub{c}H\st(T_1) + \int_{T_1}^{T_2}\!C_p(\tx{P})\dif T = 0 \tag{11.6.1} \end{equation} where \(\Delsub{c}H\st(T_1)\) is the standard molar enthalpy of combustion at the initial temperature, and \(C_p(\tx{P})\) is the heat capacity at constant pressure of the product mixture.
The value of \(T_2\) that satisfies Eq. 11.6.1 is the estimated flame temperature. Problem 11.9 presents an application of this calculation. Several factors cause the actual temperature in a flame to be lower: the process is never completely adiabatic, and in the high temperature of the flame there may be product dissociation and other reactions in addition to the main combustion reaction.