We propose here new method for calculation of the thermodynamics of adsorbed particles. Wherewith the quantum and temperature effects are taken into account. The method is based on the solution of Schrödinger equation for adsorbate and using of Gibbs distribution for particle positions and occupation of energy levels. The method is applied for investigation of hydrogen adsorption at internal and external surfaces of CNT of (10,10) and (20,0)kinds. . It is shown the ρ (P,T) does not exceed ∼3–4% (at both surfaces adsorption) at pressure up to 500 Bar and low temperatures.