11.17 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 × 103 J kg–1]
11.17 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 × 103 J kg–1]
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1 Answer
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11.17 Size of the sides of cubical ice box, s = 30 cm =0.3 m
Thickness of the icebox, l = 5 cm = 0.05 m
Mass of ice kept in the box, m = 4 kg
Time gap, t = 6 h = 6 s
Outside temperature, T = 45 °C
Coefficient of thermal conductivity of thermocole, K = 0.01 J
Heat of fusion of water, L = 335 J
Let m’ be the mass of the ice melts in 6 h
The amount of heat lost by the food: = , where
A = Surface area of the box = 6 = 6 = 0.54
= = 104976 J
We also know so m’ = 104976/ (335 = 0.313 kg
Hence the amount of ice remains
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