(a) One end of a steel rod `(K = 46 J//m-s-.^(@)C)` length `1.0 m` is kept in ice at `0^(C )` and the end is kept in boling water at `100^(@)C`. The area of cross-section of the rod is `0.4 cm^(2)`. Assuming no heat loss to atmosphere, find the mass of of the ice melting per second. Latent heat of fusion of ice `= 3.36 xx 10^(5) J//kg`
(b) An icebox almost completely filled with ice at `0^(@)C` is dipped into a large volume of water at `20^(@)C`. The box has walls of surface area `2400 cm^(2)`, thickness `2.0 mm` and thermal conductivity `0.6 W//m-^(@)C`. Calculate the rate at which the ice melts in the box. Latent heat of fusion if ice `= 3.4 xx 10^(5) J//kg`.

Explanation

`R = (l)/(KA) = (1)/(46 xx 0.04 xx 10^(-4)) = (10^(6))/(184) .^(@)C//W`
`i= (100 - 0)/(R ) = (100)/(10^(6)) xx 184 = 184 xx 10^(-4) W`
`i= m L_(ice)`
`184 xx 10^(-4) = m xx 3.36 xx 10^(5)`
`m = 54.8 xx 10^(-9) kg//s`
(b) `R = (l)/(KA) = (2 xx 10^(-3))/(0.06 xx 2400 xx 10^(-4)) = 0.14 .^(@)C//W`
`i = (20 - 0)/(R ) = (20)/(0.14) = (1000)/(7) W`
`i = mL_(ice)`
`(1000)/(7) = m xx 3.36 xx 10^(5)`
`m = 42.5 xx 10^(-5) kg//s`