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One end of an aluminium rod of length 2.35 m and radius 2.0 cm (K = 235 W/m/K) is kept at 20 deg C while the other end touches ice at its melting point. At what rate (in kg/s) does the ice melt? Take latent heat of fusion of ice = (10/3) x 10⁵ J/kg.

1. 48*pi x 10⁻⁶
2. 24*pi x 10⁻⁶
3. 2.4*pi x 10⁻⁶
4. 4.8*pi x 10⁻⁶

Correct answer: 2.4*pi x 10⁻⁶

Solution

dQ/dt = K*A*dT/L = 235*pi*4e-4*20/2.35 = 0.8*pi W; dividing by Lf gives dm/dt = 2.4*pi x 10⁻⁶ kg/s.

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