Eli5 does size of crucible matters ?

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When you try to melt a little metal in a larger crucible why does it takes much longer time . If you take more of metal in the same crucible it will melt fast . Why do you need to take a smaller one for less metal

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The only thing that will ultimately affect melting speed is the rate of heat transfer. The crucible will only be transferring heat to the contents if it itself is hot. If a crucible is larger, it could take longer to heat up, which would lead to larger melting times. Additionally, if heat is directly added via a torch from the top, a smaller crucible would possibly keep the contents in a smaller area, and take more of that heat.

In general though, if the crucible is already heated before adding anything, there shouldn’t be much of a difference. (barring a crucible that’s too big for the heater)

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).

Heat Capacity and Thermal Conductivity play important roles.

Heat capacity matters because both the metal and the crucible need to absorb energy in order to increase in temperature. (And you need the metal to reach sufficiently high temperature before it will melt.)

Thermal conductivity matters because the metal in the crucible transfers heat to the crucible; if it transfers heat very well then you are essentially heating both at the same time until they both reach the melting point of the metal. (i.e. you’re not heating *just* the small amount of metal, although that would be ideal and most perfectly efficient.)