The exact form of the spectral line weighted-sum-of-gray-gases (SLW) model is developed as a limiting case of the classical SLW method when the number of gray gases in the classical model approaches infinity. Solutions of the exact SLW radiative transfer equation are obtained in the case of isothermal media. It is demonstrated that the accuracy of the exact SLW method is limited only by the accuracy of the absorption-line blackbody distribution function (ALBDF) correlations used for the characterization of the absorption spectrum. This work also theoretically and rigorously demonstrates for the first time the relationship among the SLW, absorption distribution function (ADF), and full spectrum k-distribution (FSK) models. The theoretical foundation is laid for the extension of the exact method in the case of nonisothermal media.

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