Some gases like carbon dioxide and water will absorb radiation and re-emit radiation. These calculation are complex. The formulas used here are the ones described by Hotell and Sarofin "Radiative Heat Transfer".
The gas emissivity is calculated only if furnace dimensions are given e.g. the mean beam length can be calculated. The graph below shows the gas emissivity for a 1:1 ratio of carbon dioxide and water vapor (valid for most for fuel oils).
