If you’re starting with cold crucibles, then it just takes that much longer for a larger crucible to heat up enough that its contents melt. If the crucibles are already heated, then you’re dealing with the larger crucible radiating heat over a larger total surface area, only a small portion of which is in contact with the metal you’re trying to melt. With a smaller crucible, not only is there a smaller surface area to radiate heat, more of that surface area is in contact with the metal (as a ratio of contact area to non-contact area).
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