A metallic cylindrical vessel whose inner and outer radii are `r_1 and r_2` is filled with ice at `0^@C`. The mass of the ice in the cylinder is m. Circular portions of the cylinder is sealed with completely adiabatic walls. The vessel is kept in air. Temperature of the air is `50^@C`. How long will it take for the ice to melt completely. Thermal conductivity of the cylinder is K and its length is l. Latent heat of fusion of L.

Answer

A, B

Explanation

Consider a differential cylinder

`H = (dQ)/(dt) = KA (d theta)/(dr) = (2piKrl)(d theta)/(dr)`
`:. H/(2piKl) int_(r_1)^(r_2) (dr)/r = int_(0)^50 d theta`
or `H/(2piKl) In (r_2/r_1) = 50`
`:. H = (100piKl)/(In(r_2//r_1))`
Now, `Ht = mL`
`:. t = (mL)/H = (mL In (r_2//r_1))/(100piKl)`