Carbon sequestration in unmineable coal seams has been proposed as one of the most attractive technologies to mitigate carbon dioxide (CO₂) emissions in which CO₂ is stored in the microporous structure of the coal matrix in an adsorbed state. The CO₂ adsorption process is hence considered one of the more effective methodologies in environmental sciences. Thus, adsorption isotherm measurements and modelling are key important scientific measures required in understanding the adsorption system, mechanism, and process optimization in coalbeds. In this paper, three renowned and reliable adsorption isotherm models were employed including Langmuir, Freundlich, and Temkin for pure CO₂ adsorption data, and the extended-Langmuir model for multicomponent, such as flue gas mixture-adsorption data as investigated in this research work. Also, significant thermodynamics properties including the standard enthalpy change (\(\Delta H^\circ\)), entropy change (\(\Delta S^\circ\)), and Gibbs free energy (\(\Delta G^\circ\)) were assessed using the van’t Hoff equation. The statistical evaluation of the goodness-of-fit was done using three (3) statistical data analysis methods including correlation coefficient (R²), standard deviation (σ), and standard error (SE). The Langmuir isotherm model accurately represent the pure CO₂ adsorption on the coals than Freundlich and Temkin. The extended Langmuir gives best experimental data fit for the flue gas. The thermodynamic evaluations revealed that CO₂ adsorption on the South African coals is feasible, spontaneous, and exothermic; and the adsorption mechanism is a combined physical and chemical interaction between the adsorbate and the adsorbent.