This study presents an approximate solution for assessing radiation heat exchange within a gaseous participating medium consisting of H2O and CO2 This solution is applicable for values of the product of the total pressure and the mean beam length (PL), ranging from 0.06 to 20 atm <middle dot> m , and temperatures (T) ranging from 300 K to 2100 K. To approximate the exact solutions, the Spence root weighting method is employed. The exact spectral emissivity and absorptivity epsilon A and aA of the gas mixture for each set of PL and T values are calculated using the analytical solution (AS). Additionally, the values of the emissivity and absorptivity of the mixture epsilon m y am are determined using the Hottel graphical method (HGM) and the proposed approximate solution. The HGM shows a weaker correlation, with mean errors of + 15% and + 20% for 54.2% and 75.3% of the evaluated data, respectively. In contrast, the proposed method yields the best fit, with mean errors of + 10% and + 15% for 79.4% and 98.6% of the evaluated data, respectively. In all cases, the agreement between the proposed model and the available experimental data is deemed sufficiently robust to warrant consideration for practical design applications.