A cylindrical alumina crucible has outside dimensions of $17cm$ diameter and $30cm$ height. The wall thickness of the crucible is $1cm.$ The alumina is pure $-$alumina at $95\%$ of theoretical

density, and is preheated to $300C.$ Molten cobalt is poured into the crucible to a depth of $20cm.$

The aim is to have a final cobalt temperature of $1500C.$ Calculate the required initial cobalt temperature. The specific gravity of liquid cobalt is $7\mathrm{.}76.$ Neglect heat loss.