Final answer:
The correct term for the soldering and brazing method where the whole part must withstand heating without damage is 'furnace.' In furnace soldering, the entire workpiece is uniformly heated inside a furnace.
Step-by-step explanation:
The correct word to fill in the blank in the question “In the _______ soldering and brazing method, the entire part must be able to withstand heating without burning.” is “furnace.” Furnace soldering and brazing involve the use of a furnace to heat the metal parts and the filler metal to create a joint. Unlike other methods where localized heating may be applied, in furnace soldering, the entire workpiece is uniformly heated within a furnace. This method requires that the whole part withstand the heat without any damage or deformation, making it suitable for parts that are not heat-sensitive. It is often used for mass production or when consistent heating of the entire part is necessary.