The adsorption of methane and carbon dioxide on two microwave-activated carbon samples at different temperatures from 298 K to 323 K, and the thermodynamics of adsorption have been investigated using a vacuum adsorption apparatus. Henry's law constant and adsorption equilibrium selectivity of CO2 and CH4 on the two samples were calculated via Virial equation. The results showed that the activated carbon modified by potassium carbonate sample has the higher equilibrium selectivity for CO2 over CH4. The adsorption equilibrium data of CO2 and CH4 at various temperatures were fitted to Langmuir and Langmuir-Freundlich isotherm models. It was found the Langmuir model was better for fitting the adsorption of CH4 than CO2 and the Langmuir-Freundlich model was more suitable for description of the two gases adsorption process than Langmuir model through calculating average absolute relative error. The fitted results showed that the adsorption of CH4 was monolayer and CO2 was multilayer adsorption on the surface of two adsorbents. The isosteric enthalpies of adsorption for both adsorbates on microwave-activated carbon (MAC) and microwave-activated carbon modified with potassium carbonate (K2CO3/MAC) were calculated using the Clausius-Clapeyron equations. The isosteric heat of adsorption decreased with an increase of the surface loading on adsorbents, which means that both of MAC and K2CO3/MAC had an energetically heterogeneous surface. (C) 2012 Elsevier B.V. All rights reserved.