(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 ofthe 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.

(a) One end of a steel rod (K = 46 J//m-s-.^(@)C) length 1.0 m is kept

1.	(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 ofthe 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.
Answer» Solution :`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`