A ‘thermacole’ icebox is a cheap and 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 `= 335xx 103 J kg^(–1)]`

Explanation

Area of six faces of the box`=6l^2=6xx(0.30)^2=0.54m^2`
and `L=5.0cm=0.05cm`
time, `t=6hr=6xx3600s`
`T_1-T_2=45-0=45^@C`
Total heat entering into the box in 6 hr
`Q=(KA(T_1-T_2))/(L)`
`=(0.01xx0.54xx45xx6xx3600)/(0.05)=104976J`
If m be the amount of ice melted then
`Q=mL`
or `m=(Q)/(L)=(104976)/(335xx10^3)=-.313kg`
Mass of the ice left after `6h=(4-0.313)kg`
`=3.687kg`