Due to cold weather, a 1 m water pipe of cross-sectional area 1 cm 2 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 × 10 5 J kg - 1 , specific heat of ice = 2 × 10 3 J kg -

Step-by-step solution

The mass of ice, m = ρ A L = 10 3 × 10 - 4 × 1 = 10 - 1   kg , Energy required to melt the ice, = m S Δ T + m L , ⇒ i 2 R t = m S Δ T + m L ⇒ ( 1 ) 2 × 10 3 × t = 10 3 × 1 × 10 - 4 × 2000 × 10 + 10 3 × 1 × 10 - 4 × 330 × 10 3 ⇒ ( 1 ) 2 × 10 3 × t = 3 . 53 × 10 4 ⇒ t = 35 . 3   s