To help prevent frost damage, fruit growers sometimes protect their crop by spra

Question

To help prevent frost damage, fruit growers sometimes protect their crop by spraying it with water when overnight temperatures are expected to go below the freezing mark. When the water turns to ice during the night, heat is released into the plants, thereby giving them a measure of protection against the falling temperature. Suppose a grower sprays 7.34 kg of water at 0°C onto a fruit tree. (a) How much heat is released by the water when it freezes? (b) How much would the temperature of a 136-kg tree rise if it absorbed the heat released in part (a)? Assume that the specific heat capacity of the tree is 2.5 x 103 J/(kg C°) and that no phase change occurs within the tree itself.

Explanation / Answer

Since heat of fusion of ice is not given, its value is being taken from standard values i.e. 333.55kJ/kg.Since here it is 7.34 kg, so

a) Heat released by the water when it freezes= 333.55*7.34= 2448.257*10^3 J

b) Now, 2448.257kJ is released into the plants, so, 2448.257*10^3 J= 136 kg* 2.5*10^3 J/kg0C* temperature rise in 0C

or, Temperature rise of a 136-kg tree if it absorbed the heat released in part (a)= 7.2 0C

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