The emission of radiation from diatomic gases. III. Numerical emissivity calculations for carbon monoxide for low optical densities at 300°K and atmospheric pressure

Numerical emissivity calculations at 300°K and atmospheric pressure for nonoverlapping rotational lines have been carried out for CO using a dispersion formula for the line-shape representation. Use of the best available experimental data on integrated absorption and rotational line-width leads to calculated emissivities which are in excellent agreement with extrapolated empirical data published by Hottel and Ullrich. In particular, the theoretical dependence of emissivity on optical density, for small optical densities at 300°K, has been shown to follow experimental observations with satisfactory precision.For small optical densities the calculated emissivity is found to be proportional to the square root of the assumed rotational line-width, thus emphasizing the need for accurate line-width determinations at elevated temperatures. The limits of validity of the treatment utilizing nonoverlapping rotational lines are defined by examining overlapping between adjacent weak and strong rotational lines.The calculation of emissivities can be simplified by the use of approximate treatments. Thus absolute values of the emissivity can be predicted within 10 percent by utilizing a treatment for nonoverlapping, equally spaced, and equally intense lines, together with empirically determined values for the equivalent mean integrated absorption of the rotational lines of CO. A better analytic solution, which does not involve the assumptions of equal spacing and equal intensity of the rotational lines, has been obtained by utilizing asymptotic relations for large values of modified Bessel functions