A new approach to constructing adsorption thermodynamics that provides the derivation of rigorous thermodynamic relationships for any adsorption system, particularly for a system with a deformable adsorbent, is proposed. Expressions for the thermodynamic functions of an adsorption system in the form of an arbitrary control volume containing the adsorbent and the adsorbed gas are derived. In the derived expressions, the role of adsorption is played by the total adsorbate content in the system. If the control volume boundaries are set appropriately, this quantity is identical to absolute adsorption.