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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 all the heat produced is used for melting, what is the minimum time required ? (Given latent heat of fusion of water/ice = 3.33 × 10⁵ J kg⁻¹, specific heat of ice = 2 × 10³ J kg⁻¹ and density of ice = 10³ kg/m³)

1. 0.353 s
2. 35.3 s
3. 3.53 s
4. 70.6 s

Correct answer: 35.3 s

Solution

The correct option is 35.3 s because the total energy required to melt the ice includes both the energy to raise the temperature of the ice to 0°C and the energy to melt it. The power generated by the resistive heating is calculated using the formula P = I²R, and the total time is determined by dividing the total energy by the power, leading to the correct time of 35.3 seconds.

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