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An ice cube of dimensions 60 cm × 50 cm × 20 cm is placed in an insulation box of wall thickness 1 cm. The box keeping the ice cube at 0°C of temperature throughout a room of temperature 40°C. The rate of melting of ice is approximately. (Latent heat of fusion of ice is 3.4 × 10⁵ J kg⁻¹ and thermal conductivity of insulation wall is 0.05 Wm⁻¹°C⁻¹)

1. 61 × 10⁻⁵ kg s⁻¹
2. 61 × 10⁻⁵ kg s⁻¹
3. 208 kg s⁻¹
4. 30 × 10⁻⁵ kg s⁻¹

Correct answer: 61 × 10⁻⁵ kg s⁻¹

Solution

The correct option is based on the calculation of heat transfer through the insulation wall, which determines the rate at which energy is supplied to the ice cube. By applying Fourier's law of heat conduction and using the latent heat of fusion, we find that the melting rate corresponds to the calculated heat transfer, confirming the answer.

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