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)]`

Answer

`3.739` kg

Explanation

`Q = KA((theta_(1) - theta_(2)) t)/(l) = mL`
`implies m xx 335 xx 10^(3)`
=`0.01 xx (0.54 xx 45 xx6 xx 60 xx 60)/(5 xx 10^(-2))`
`implies m = 0.261`kg
Therefore mass of ice left in the box after `6` hours = `( 4 - 0.261) kg = 3.739`kg