Spectroscopic and Theoretical Determination of Flame Temperature
Jonathan Smith
In this investigation we will consider the
temperature of flames theoretically and compare our findings with our own
experimental findings. The theoretical model is known as the adiabatic flame
approximation. In this approximation all the heat generated through combustion
is transferred to the gases occupying the flame volume in their stoichiometric
ratios. The temperature rise and equilibrium temperature is computed by using
temperature dependent heat capacities of each component (CO2 , H2O,
and N2) and the assumption that no heat is transfered to the
surroundings (adiabatic). We will experimentally determine the temperature of
various flames by monitoring the spectrum (intensity vs. wavelength) of
radiation emitted by a flame. In order to make this determination we need to
assume certain theoretical models. In one method we can assume that the
radiation emitted from a flame can be treated as ideal black-body radiation. A
black-body is an object that is capable of emitting and absorbing all
wavelengths of light equally well. The concept of an ideal black-body radiator
is covered in McQuarrie and Simon. Experimental observation of black-body
radiation was one observation that could not be explained by classical physics
which predicted that the intensity of light from any heat object would increase
without bounds in the ultraviolet portion of the electromagnetic spectrum. This
was labeled the ultraviolet catastrophe and was the successful explanation of
this phenomena was one of the first successes of the new quantum theory
emerging at the turn of the century. A nice discussion of this phenomena is
given in a Web page at the
In our investigation, we will use a more
accurate spectroscopic probe of temperature, high resolution spectroscopy of the
emission of OH radicals formed in the flame.
In the flame emission occurs from electronically excited OH radical in
the A 2å to the ground state X 2Õ. At 306.4 nm
the transition is between the zero-point vibrational level of the excited state
(v’=0) to the zero-point vibrational level of the ground electronic state
(v’’=0). Rotational transitions are
superimposed on these vibrational levels leading to a highly structured
spectrum. The structure corresponds to
these rotational transitions with intensities corresponding to a number of
factors including the number of molecules in the initial rotational state which
in turn is related to temperature. We
will use reference intensities for a 3000 K flame tabulated by Izarra (J. Phys. D: Appl. Phys. 33 (2000) 1697-1704). The spectrum will be recorded on various
flames in the laser laboratory using a high resolution fiber optic coupled
spectrograph with a LN2 cooled CCD detector. The analysis will proceed with the aid of the
article by Izarra and a template Excel spreadsheet (download).
Preparation: As background for the experimental portion, read UV OH spectrum used as a molecular pyrometer, by Charles de Izarra (J. Phys. D: Appl. Phys. 33 (2000) 1697-1704). In order to do the theoretical calculations we need to assume that the area of the flame in which the combustion reactions are taking place is adiabatically separated, no heat transfer, from the area outside the flame for the instant at which we carry out a theoretical calculation. Write out the balanced equations for combustion of each of the following alcohols. Calculate the heat of combustion for each compound using WebMO and your favorite computational model chemistry (AM1 or PM3).
Compounds
|
octanol |
|
ethanol |
|
methanol |
|
butanol |
Steps
- By
examining the Chevron
MSDS of Jet Fuel A determine the major components of jet fuel and
carry out a Mathcad calculation (described later) on the largest
component. The combustion process provides the propulsion for jets. The
theory is discussed nicely on a Web site
at the
- We will take turns recording the OH radical emission spectrum of various alcohol flames using a spectrograph and a LN2 cooled CCD detector both interfaced to a computer. Files will be stored at http://zeke.chem.gac.edu/data/2006/pchem.
- Mathcad
is a comprehensive mathematical package which facilitates numeric and
symbolic computation. It will be of great use in problem solving in class
and in the laboratory. To become accustomed to working with Mathcad we
will work through a Mathcad document, Mathcadintro.mcd
It will be necessary to obtain temperature dependent heat capacities from the NIST Webbase. Note: The values of A, B, C, D, and E for the Shomate equation from NIST must be multiplied by 100, 10-3, 10-6, 10-9, and 105 respectively. - A Mathcad worksheet, Flame.mcd, will help us make a theoretical estimate of the temperature of various flames based on the adiabatic approximation.
- A
helpful Web page is at the
- Compare the theoretical and experimental (through theidealized Black-body radiation model) using the equation given in the above Web page or the equation from Atkins above.
- Compare values with at least two other groups for different flames.
- What seem to be the most important factors in determining flame temperature or is there a missing parameter?
- Can you think of a reason why the experimental value might deviate from the theoretical?
- Turn in a carefully formatted spectrum of your flames emission.
