Current Electricity

Due to cold weather a 1 m water pipe of cross-sectional area 1 cm² is filled with ice at \(-\)10\(^\circ\)C. Resistive heating is used to melt the ice. Current of 0.5A is passed through 4 k\(\Omega\) 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 \(\times\) 10⁵ J kg^\(-\)1, specific heat of ice = 2 \(\times\) 10³ J kg^\(-\)1 and density of ice = 10³ kg/m³