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 `2400cm^(2)` thickness `2.0mm` and thermal conductivity `0.06Wm^(-1)C^(-1)` . Calculate the rate at which the ice melts in the box. Latent heat of fusion of ice `=3.4xx10^(5)Jkg^(-1)` .

Answer

A

Explanation

`A=2400 cm^(2)=2400xx10^(-4) m^(2)`,
`L=2mm=2xx10^(-3)m,K=0.06W//m-^(@)C.`
`T_(1)=20^(@)C`,`T_(2)=0^(@)C`.
`(Q)/(T)=(kA(T_1-T_2))/(l)`
`(0.06xx2400xx10^(-4)xx20)/(2xx10^(-3))`
`=(6xx10^(2)xx24xx10^(2)xx10^(-4)xx20)/(2xx10^(-3))`
`24xx6xx10^(-1)xx101`
`=24xx6=144 J//see`.
`Rate in which ice melts
`=m/t=(Q)/(txxl)=(144xx3600)/(3.4xx10^(5))kg/h.`
`=1.52kg/h`