Cool and dense ejections, typically Hα surges, often appear alongside EUV or X-ray coronal jets as a result of the emergence of magnetized plasma from the solar interior. Idealized numerical experiments explain those ejections as being indirectly associated with the magnetic reconnection taking place between the emerging and preexisting systems. However, those experiments miss basic elements that can importantly affect the surge phenomenon. In this paper we study the cool surges using a realistic treatment of the radiation transfer and material plasma properties. To that end, the Bifrost code is used, which has advanced modules for the equation of state of the plasma, photospheric and chromospheric radiation transfer, heat conduction, and optically thin radiative cooling. We carry out a 2.5D experiment of the emergence of magnetized plasma through (meso) granular convection cells and the low atmosphere to the corona. Through detailed Lagrange tracing we study the formation and evolution of the cool ejection and, in particular, the role of the entropy sources; this allows us to discern families of evolutionary patterns for the plasma elements. In the launch phase, many elements suffer accelerations well in excess of gravity; when nearing the apex of their individual trajectories, instead, the plasma elements follow quasi-parabolic trajectories with accelerations close to {g}ȯ . We show how the formation of the cool ejection is mediated by a wedge-like structure composed of two shocks, one of which leads to the detachment of the surge from the original emerged plasma dome.