Question

A metallic cylindrical vessel whose inner and outer radii are $r_1$ and $r_2$ is filled with ice at $0^{o}C$. The mass of the ice in the cylinder is $m$. Circular portion of the cylinder is sealed with completely adiabatic walls. The vessel is kept in air. Temperature of the air is ${50}^{o}C$. How long will it take for the ice to melt completely? Thermal conductivity of the cylinder is $k$, length is $l$ and latent heat of fusion is $L$.

Answer 1

Heat required $Q=mL$

$\frac{Q}{t}=\frac{2\pi ll({\theta }_1-{\theta }_2)}{ln\left(r_2/r_1\right)}\therefore \frac{mL}{t}=\frac{2\pi lk50}{ln\left(r_2/r_1\right)}\Rightarrow t=\frac{mL.ln\left(r_2/r_1\right)}{100\pi lk}$