A hollow sphere of glass whose external and internal radii are `11cm` and `9cm` respec-tively is completely filled with ice at `0^(@)C` and placed in a both of boiling water How long will it take for the ice to melt completely ? Givne that density of ice `=0.9g//cm^(3)` latent heat of fusion of ice `=80 cal//g` and thermal conductivity of glass `=0.002 cal//cm-s^(@)C` .

Explanation

In steady state, rate of heat flow `H =(4piKr_(1)r_(2)Deltatheta)/(r_(2)-r_(1))`
Substituting the values
`H=((4)(pi)(0.002)(11)(9)(100-0))/((11-9))` or
`(dQ)/(dt) =124.4cal//s,(dQ)/(dt) = L (dm)/(dt)` ltbr gt `:.((dm)/(dt)) =(dQ//dt)/(L) = (124.4)/(80) =1.555g//s`
Total mass of ice `m =rho_(ice) (4pi r_(1)^(2)) = (0.9) (4) pi(9)^(2)`
`:.` Time taken for the ice to melt completely
`t = (m)/((dm//dt)) = (916)/(1.555) =589s` .