The Metal spade without a handle is a quest item used during the Miss Cheevers section of the Recruitment Drive quest. It is made by burning a full metal spade with a bunsen burner to remove the handle. It can then be used on the door to place it into a hole. Adding cupric sulphate and dihydrogen monoxide will heat the spade, expanding the metal and trapping it in the hole, at which point it can then be used as a handle to open the door.
Once it is used, it cannot be taken out of the door, however you can make another one. It cannot be taken out of the room, as with any other items acquired within the tests.