One end of a 2.35 m long aluminium rod of radius 2.0 cm and thermal conductivity K=235 W m⁻¹ K⁻¹ is held at 20°C. The other end is in contact with ice at 0°C. Find the melting rate of ice in kg s⁻¹. Take latent heat of fusion of ice L=(10/3)×10⁵ J kg⁻¹.
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Question

One end of a 2.35 m long aluminium rod of radius 2.0 cm and thermal conductivity K=235 W m⁻¹ K⁻¹ is held at 20°C. The other end is in contact with ice at 0°C. Find the melting rate of ice in kg s⁻¹. Take latent heat of fusion of ice L=(10/3)×10⁵ J kg⁻¹.

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G1 Physics · Accepted Answer

In steady conduction, heat current is H=kAΔT/L. Treat each segment as a thermal resistance Rₜₕ=L/(kA); series resistances add and parallel heat currents add. Evaluating the given data/statements gives C: 2.4π ×10⁻⁶. Therefore the correct answer is C.