This study investigated the behavior of a non-isothermal $CO_2$ bubble formed through a leak process from a high-pressure source in a deep sea. Isenthalpic interpretation was employed to predict the state of the bubble just after the leak. Three modes of mass loss from the rising bubble were demonstrated: dissolution induced by mass transfer, condensation by heat transfer and phase separation by pressure decrease. A graphical interpretation of the last mode was provided in the pressure-enthalpy diagram. A threshold pressure (17.12 bar) was identified below which the last mode was no longer present. The second mode was as effective as the first for a bubble formed in deep water, leading to faster mass loss. To the contrary, only the first mode was active for a bubble formed in a shallow region. The third mode was insignificant for all cases.