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 8.09 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 197-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

here,

mass of water , mw = 8.09 kg

initial temprature , Ti = 0 degree C

(a)

heat released when it freezes , H = mw * latent heat of fusion

H = 8.09 * 334 KJ

H = 2702.06 KJ

the heat energy released is 2702.06 KJ

(b)

let the change in temprature of tree be T

mass of tree , mt = 197 kg

heat capacity of tree , Ct = 2.5 KJ/(kg . degree C)

heat energy = mt * T * Ct

2702.06 = 197 * T * 2.5

T = 5.49 degree C

the temprature of the tree rises 5.49 degree C

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