A cylindrical rod with one end in a steam chamber and the other end in ice results in melting of $0.1 \mathrm{g}$ of ice per second. If the rod is replaced by another with half the length and double the radius of the first and if the thermal conductivity of the material of the second rod is $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$ that of the first, the rate at which ice melts in $\mathrm{g} {\mathrm{s}}^{-1}$ will be