One end of a copper rod of length 1.0 m and area of cross-section $ {{10}^{-3}}{{m}^{2}} $ is immersed in boiling water and the other end in ice. If the coefficient of thermal conductivity of copper is $ 92\text{ }cal\text{/}m-s\text{ }{}^\circ C $ and the latent heat of ice is $ 8\times {{10}^{4}}cal\text{/}kg, $ then the amount of ice which will melt in one minute is: