In the figure shown, $\mathrm{AB}$ is a rod of length $30 \mathrm{~cm}$, area of cross-section $1 \mathrm{~cm}^2$ and thermal conductivity $336 \mathrm{SI}$ units. The ends $\mathrm{A}$ and $\mathrm{B}$ are at constant temperatures $20^{\circ} \mathrm{C}$ and $40^{\circ} \mathrm{C}$ respectively. A point $\mathrm{C}$ of the rod is connected to ice at $0^{\circ} \mathrm{C}$ in a thermally insulated box $\mathrm{D}$ through a highly conducting wire of negligible heat capacity. The rate at which ice melts in the box is $\left(\mathrm{L}_{\mathrm{ice}}=80 \mathrm{cal} \mathrm{g}^{-1}\right)$