$1.$ A $24-$g ice cube floats in $230$ g of water in a $100-$g copper cup; all are at a temperature of$0\backslash$deg C$.$ A piece of lead at $86\backslash$deg C is dropped into the cup, and the final equilibrium temperature is$12\backslash$deg C$.$ What is the mass of the lead? $($The heat of fusion and specific heat of water are $3\mathrm{.}33$ x $105$ J$/$kg and $4,186$ J$/$kg $\backslash$deg C$,$ respectively. The specific heat of lead and copper are $128$ and $387$ J$/$kg $\backslash$deg C$,$ respectively.$)$