The PIAVE injector for the Legnaro Accelerator complex is an accelerating machine made of superconducting resonators. One of them, the superconducting RFQ, needs to be cooled by the helium bath on the whole outer surfaces. In particular the region of the electrode tips and the lower vertical electrode are involved in RF power dissipation and can have a trapped volume of liquid. During the operation the liquid evaporates and the produced gas needs to be evacuated, in order to cool the structure properly. The problem of gas production and evacuation from a trapped volume of liquid helium has been studied and solved. Studies of the possible evacuation systems and experimental apparatus are presented.