page_title: Adiabatic flame temperature
section_title: Thermodynamics
hierarchical_section_title: Adiabatic flame temperature / Thermodynamics
context_page_description: In the study of combustion, there are two types of adiabatic flame temperature depending on how the process is completed: the constant volume and constant pressure; both of which describe temperature that combustion products theoretically can reach if no energy is lost to the outside environment.
  The constant volume adiabatic flame temperature is the temperature that results from a complete combustion process that occurs without any work, heat transfer or changes in kinetic or potential energy. Its temperature is higher than the constant pressure process because no energy is utilized to change the volume of the system.
context_section_description: From the first law of thermodynamics for a closed reacting system we have,
  where,  and  are the heat and work transferred from the system to the surroundings during the process respectively, and  and  are the internal energy of the reactants and products respectively. 
  In the constant volume adiabatic flame temperature case, the volume of the system is held constant hence there is no work occurring,
  and there is no heat transfer because the process is defined to be adiabatic: .  As a result, the internal energy of the products is equal to the internal energy of the reactants: .  
  Because this is a closed system, the mass of the products and reactants is constant and the first law can be written on a mass basis,
  .
  In the constant pressure adiabatic flame temperature case, the pressure of the system is held constant which results in the following equation for the work,
  Again there is no heat transfer occurring because the process is defined to be adiabatic: .  From the first law, we find that,
  Recalling the definition of enthalpy we recover: .  Because this is a closed system, the mass of the products and reactants is constant and the first law can be written on a mass basis,
  .
  We see that the adiabatic flame temperature of the constant pressure process is lower than that of the constant volume process.  This is because some of the energy released during combustion goes into changing the volume of the control system.
  If we make the assumption that combustion goes to completion (i.e. CO
  ₂ and H
  ₂O), we can calculate the adiabatic flame temperature by hand either at stoichiometric conditions or lean of stoichiometry (excess air).  This is because there are enough variables and molar equations to balance the left and right hand sides,
  Rich of stoichiometry there are not enough variables because combustion cannot go to completion with at least CO and H
  ₂ needed for the molar balance (these are the most common incomplete products of combustion),
  However, if we include the Water gas shift reaction,
  and use the equilibrium constant for this reaction, we will have enough variables to complete the calculation.
  Different fuels with different levels of energy and molar constituents will have different adiabatic flame temperatures.
  We can see by the following figure why nitromethane (CH₃NO₂) is often used as a power boost for cars.  Since each molecule of nitromethane contains two atoms of oxygen, it can burn much hotter because it provides its own oxidant along with fuel. This in turn allows it to build up more pressure during a constant volume process.  The higher the pressure, the more force upon the piston creating more work and more power in the engine.  It stays relatively hot rich of stoichiometry because it contains its own oxidant.  However, continual running of an engine on nitromethane will eventually melt the piston and/or cylinder because of this higher temperature.
  In real world applications, complete combustion does not typically occur.  Chemistry dictates that dissociation and kinetics will change the relative constituents of the products.  There are a number of programs available that can calculate the adiabatic flame temperature taking into account dissociation through equilibrium constants (Stanjan, NASA CEA, AFTP).  The following figure illustrates that the effects of dissociation tend to lower the adiabatic flame temperature.  This result can be explained through Le Chatelier's principle.
caption: Enthalpy versus temperature diagram illustrating closed system calculation
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