Steve Williams
Chemistry Department
Appalachian State University
ASU Chemistry
Boone, NC 28608
willsd@zardoz.chem.appstate.edu
Adiabatic Flame Temperature: A Computational Physical
Chemistry Experiment
Most physical chemistry textbooks include a discussion of combustion
reactions and how the adiabatic approximation can be used to estimate
the temperatures of flames in such reactions. The assumption used is
that all of the heat generated by the reaction is absorbed by the
combustion products. Hence if the heat is known (and it can easily be
calculated from tabulated data) and if the heat capacity of the
products is known, then the final temperature can be calculated. The
major complication is that as the temperature of the products
increases, their heat capacity changes as well. The usual method (not
what is used here) described in most texts for including the
temperature dependence of the heat capacity is to use an empirically
determined polynomial to describe this temperature variation. When
this is integrated to find the total heat absorbed by the products, the
final temperature (the adiabatic flame temperature) is a root of the
integrated polynomial. This is usually simplified by just including
the constant and linear terms in the heat capacity expression, so that
the resulting integrated expression is at worst a quadratic equation,
whose roots are readily found. In this project a more
sophisticated treatment of the temperature dependence of the heat
capacity is used. This treatment is based on simple statistical
mechanics and includes the contributions to the heat capacity from
translational, rotational, and vibrational motions of the product gas
molecules. The resulting expression may be integrated in closed form,
but the integral is a rather messy transcendental equation that must be
solved for the flame temperature. The solution is found by using a
root finding program. While many methods for this are available, the
project describes a solution using bisection. This method is used
because it is simple to explain, is quite reliable, and is easy to
code.
Last modified: 17 July, 1997
Thomas L. Marchioro
uces_info@krellinst.org