Question

One end of a $2.35m$ long and $2.0cm$ radius aluminium rod $(K=235W.m^{-1}{K}^{-1})$ is held at ${20}^{\circ }C$. The other end of the rod is in contact with a block of ice at its melting point. The rate in $kg.s^{-1}$ at which ice melts is :

(Latent heat of fusion = $336\times {10}^{3}J/kg$)

• A. $48\pi \times {10}^{-6}$
• B. $24\pi \times {10}^{-6}$
• C. $2.4\pi \times {10}^{-6}$
• D. $4.8\pi \times {10}^{-6}$

Answer 1

The correct option is C $2.4\pi \times {10}^{-6}$

Rate of heat transfer is $Q/t=K\times \left(\pi r^2\right)\times \Delta T/L=235\times \pi \times 4\times {10}^{-4}\times (20-0)/2.35=0.8\pi J{s}^{-1}$

Latent heat of fusion is $336\times {10}^{3}J/kg$

So rate of melting of ice is $0.8\pi /336\times {10}^{3}kg.s^{-1}=2.38\pi \times {10}^{-6}kg.s^{-1}$