Due to cold weather a 1 m water pipe of cross–sectional area 1 cm2 is filled with ice at –10°C. Resistive heating is used to melt the ice. Current of 0.5 A is passed through 4 kΩ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required ?
(Given latent heat of fusion for water/ice $=3.33 \times 10^5 \mathrm{~J} \mathrm{~kg}^{-1}$, specific heat of ice $=2 \times 10^3 \mathrm{~J} \mathrm{~kg}^{-1}$ and density of ice $=10^3 \mathrm{~kg} / \mathrm{m}^3$