Free piston apparatus, comprising: - a piston receptacle having an axis, wherein the piston receptacle comprises or forms a combustion chamber delimited by a wall arrangement in which at least one inlet opening for the supply of fresh gas and, spaced apart therefrom in an axial direction, at least one outlet opening for the removal of exhaust gas are formed, - at least one piston device having a piston being arranged in the piston receptacle so as to be reciprocable along the axis, - a cooling device arranged on the piston receptacle for cooling the wall arrangement, which cooling device comprises or forms a cooling channel for a cooling medium which is arranged radially outside on the wall arrangement and at least partially surrounds the same in circumferential direction of the axis, which cooling channel has a first cooling region and a second cooling region axially on opposing sides of the at least one outlet opening, characterized - in that the piston receptacle comprises or forms an outlet chamber, arranged outside on the wall arrangement, which is delimited radially inside by the wall arrangement and radially outside by an outer wall of the piston receptacle, wherein exhaust gas enters into the outlet chamber via the at least one outlet opening and an outlet conduit for exhaust gas is connected to the outlet chamber, - in that the cooling channel has at least one third cooling region which extends at least partially in circumferential direction of the axis and which flow-connects the first cooling region and the second cooling region along the axial extension of the outlet chamber and is positioned at least in sections radially outside of the outlet chamber, - in that the third cooling region is delimited at least in the region of the outlet chamber radially inside by the outer wall of the piston receptacle and radially outside by a channel wall, the cooling medium being able to flow through the third cooling region between the outer wall and the channel wall. - a piston receptacle having an axis, wherein the piston receptacle comprises or forms a combustion chamber delimited by a wall arrangement in which at least one inlet opening for the supply of fresh gas and, spaced apart therefrom in an axial direction, at least one outlet opening for the removal of exhaust gas are formed, - at least one piston device having a piston being arranged in the piston receptacle so as to be reciprocable along the axis, - a cooling device arranged on the piston receptacle for cooling the wall arrangement, which cooling device comprises or forms a cooling channel for a cooling medium which is arranged radially outside on the wall arrangement and at least partially surrounds the same in circumferential direction of the axis, which cooling channel has a first cooling region and a second cooling region axially on opposing sides of the at least one outlet opening, - in that the piston receptacle comprises or forms an outlet chamber, arranged outside on the wall arrangement, which is delimited radially inside by the wall arrangement and radially outside by an outer wall of the piston receptacle, wherein exhaust gas enters into the outlet chamber via the at least one outlet opening and an outlet conduit for exhaust gas is connected to the outlet chamber, - in that the cooling channel has at least one third cooling region which extends at least partially in circumferential direction of the axis and which flow-connects the first cooling region and the second cooling region along the axial extension of the outlet chamber and is positioned at least in sections radially outside of the outlet chamber, - in that the third cooling region is delimited at least in the region of the outlet chamber radially inside by the outer wall of the piston receptacle and radially outside by a channel wall, the cooling medium being able to flow through the third cooling region between the outer wall and the channel wall.