The authors have used differential scanning calorimetry and X-ray diffraction to study absorption and desorption of oxygen by superconducting Y₁Ba₂Cu₃O_7-x. They show that these reactions are reversible and discuss them in terms of underlying thermodynamic and kinetic processes. In particular, they measure the heat evolved during absorption of oxygen and correlate the forms of absorption peaks on DSC traces with the rate of ingress of oxygen. This rate is presumed to be limited by the speed with which oxygen atoms can diffuse through the superconducting phase. They find values for the activation energy and pre-exponential factor for diffusion of oxygen through the superconducting material and suggest guidelines for annealing treatments intended to optimise the oxygen content and superconducting properties of Y₁Ba₂Cu₃O_7-x.