An exhaust volume (20) of the type including a muffler (24) having a casing provided with an inlet (29) and an outlet (30) for passing gases and adapted to enable the muffler to be mounted in an exhaust system (14). The volume further includes an additional enclosure (26) forming an accumulation cavity communicating solely with the casing of the muffler (24) via at least one connection pipe (28), the additional enclosure (26) being placed outside the muffler (24). The additional enclosure (26) is of a structure whose ability to withstand high temperature is lower than that of the structure of the muffler (24).