Capillary condensation is important in the behaviour of various materials encountered in nature and in industrial processes. The behaviour of liquid capillary bridges has mostly been investigated from a mechanical perspective, with an emphasis on computing the relevant adhesion forces. In the present paper, a thermodynamic approach is used, computing the free energy of such systems (based on numerically constructed shapes of liquid bridges) in order to determine the nature and properties of their equilibrium states. The dependence of the thermodynamic equilibrium configurations on the geometry of the system is investigated, and comparisons are made with experimental findings reported in the literature.