Infrared Emissivity of Carbon Dioxide (4.3-µ Band)
JOSA, Vol. 53, Issue 8, pp. 951-960 (1963)
http://dx.doi.org/10.1364/JOSA.53.000951
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Abstract
Simplified equations are developed for computing the emissivity of the carbon dioxide 4.3µ, band. The harmonic oscillator model is assumed in computing band intensities, but anharmonicity is considered in computing the spectral distribution of emitted radiation. Calculated values of S¯/d and 2α_{0}^{½}S¯^{½}/d are presented for temperatures ranging from 300° to 3000°K, from which emissivities may be readily computed for a given pressure and optical path in both the weak-line and strong-line approximations. In the absence of significant Doppler broadening, both approximations provide upper limits to the emissivity. Emissivities are also computed for the case of a pure Doppler line shape for temperatures ranging from 300° to 1500°K. Doppler broadening is shown to be an important factor in setting a lower limit to the possible values of emissivity obtained at low pressures and long path lengths. Comparisons are made with published experimental data using the weak-line approximation; in several cases, the strong-line approximation as well as a mixed strong-line-weak-line approximation is also shown. The results of the present work are shown to be in good agreement with published experimental data and in definite disagreement with other theoretical calculations.
Citation
W. MALKMUS, "Infrared Emissivity of Carbon Dioxide (4.3-µ Band)," J. Opt. Soc. Am. 53, 951-960 (1963)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-53-8-951
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References
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- This approximation is based on Dennison's values (x_{13}= -21.9, x_{23}= -11.0) as given by Herzberg,^{13} and used by Plass.^{8} Courtoy's^{14} more recent measurements differ somewhat (x_{13}= 19.37, x_{23}= 12.53); however, the exactness of the approximation x_{13}≈2x_{23} is not critical since x_{13}υ_{1}+x_{23}υ_{2}≡ x¯υ+½(½x_{13}-x_{23})(2υ_{1}-υ_{2}). The second term is dropped in Eq. (6); its coefficient is small compared with x¯ (using either set of data), and the factor |2υ_{1}-υ_{2}| ≤υ. The approximation ω_{1}≈2ω_{2} is very close; however, the same remarks apply to its noncriticality.
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- Assume a statistical distribution of lines of intensity S with an arbitrary probability distribution P(S). Then we have^{8} [equation] where p is the total pressure, c the mole fraction of absorbing gas, and b(p, ω) the normalized line shape factor. If we assume the line shape to be linearly pressure broadened, but otherwise arbitrary we have b(p ω) = p^{-1}[(ω-ω_{0})/p], where f is an arbitrary function of its argument. If we change the lower limit of the integral over ω from 0 to -∞ for mathematical convenience and make the substitution u= (ω-ω_{0})/p, we find [equation] Thus In(I_{0}/I) is linear in p, although Beer's law is not satisfied in general, as is seen from the complicated functional dependence on l.
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- U. P. Oppenheim and Y. Ben-Aryeh, J. Opt. Soc. Am. 53, 344 (1963).
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