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A hollow sphere of glas whose external a...

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

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The correct Answer is:
A, D
In steady state, rate of heat flow (result is taken from Example 4)
`H = ((4piKr^1r^2DeltaT)/(r^2-r^1))`
Substituting the values, `H = ((4)(pi)(0.002)(11)(9)(100-0))/(11-9)`
`or (dQ)/(dt) = 124.4 cal//s`
This rate should be equal to, L (dm)/(dt)
`((dm)/(dt)) = (dQ//dt)/L = 124.4/80 = 1.555 g//s `
Total mass of ice, `m = rho_(ice) (4pir_(1)^2)`
`=(0.9)(4)(pi)(9)^2`
= 916g
`:.` Time taken for the ice to melt completely
`t = m /(dm//dt) = 916/1.555 = 589s `
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