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 freezing. When the water turns to ice during the night, heat is released into the plants, thereby giving a measure of protection against the cold. Suppose a grower sprays 7.0 kg of water at 0°C onto a fruit tree.

(a) How much heat is released by the water when it freezes? ____________J

(b) How much would the temperature of a 163-kg tree rise if it absorbed the heat released in part (a)? Assume that the specific heat capacity of the tree is 2.5 103 J/(kg · C°) and that no phase change occurs within the tree itself. _____________°C

Explanation / Answer

we know latent heat of fusion of ice, Lf = 3.33*10^5 J/kg

so,

a) heat released when water freezes, Q = m*Lf

= 7*3.33*10^5

= 2.33*10^6 J

b) given, mass of tree, M = 163 kg

secific heat of tree, c = 2.5*1063 J/(kg C)

let dt is the increase in temperature.

Apply, Q = M*c*dT

==> dT = Q/(M*c)

= 2.33*10^6/(163*2.5*10^3)

= 5.7 degrees celsius

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