The escape through the trash chute led to the trash compactor. Another obstacle that there doesn't seem to be any way out of and for the meantime a safe haven away from the Imperial troops.
All the trash compacted go through the incinerator which generates an ample amount of power used by the lower levels of the Death Star. Other trash brought in for disposal are fed though the main door of the incinerator. Imperial techs wear fire-resistant suits to protect themselves from the heat.