A' thermacole' icebox is a cheap and an efficient method for storing small quantities of cooked food in summer in particular. A cubical icebox of side 30 cm has a thickness of `5.0 cm. "if "4.0 `kg of ice is put in the box, estimate the amount of Ice remaining after 6 h. The outside temperature is `45^(@) C` and co-efficient of thermal conductivity of thermacole is `0.01 J s^(-1) m^(-1) K^(-1)`. [Heat of fusion of water ` = 335 xx 10^(3) J kg^(-1) `]

Explanation

Area of six faces of the box,
A = 6 `l^(2) = 6 xx (0.3)^(2) = 0.54 m^(2)`
thickness, L = 5 cm= 0.05m, time, t = 6h = 6 `xx 3600 ` S
temparature difference = 45 - 0 = `45^(0)` C
total heat entering in to the box in 6 hours.
Q = `(KA(theta_(1) - theta_(2))t)/(L)`
= ` (0.01 xx 0.54 xx 45 xx 6 xx 3600)/(0.05) = 104976 ` J
If.m be the amount of ice melted, then
`m = (Q)/(L_(ice)) = (104976)/(335 xx 10^(3)) = 0.313 `kg
`therefore` mass of ice left after 6h = 4 - 0.313 = 3.687 kg.