Question

To help prevent frost damage, 4.80 kg of 0°C water is sprayed onto a fruit tree.

(a) How much heat will be released by the water as it freezes?
kcal
(b) How much would the temperature of the 200 kg tree decrease if it lost this amount of heat, given its specific heat is 0.800 kcal/kg·°C, and no phase change occurs?
°C

Answer 1

Given 0.800 kcal/kg·°C = 3.3472 x10^3 J/kg-C
Since there is a phase change, this is a heat of fusion problem.

Heat Released = mass of water x heat of fusion of water

The heat of fusion of water is 334 kJ/kg (wikipedia article), so:

Heat released = 1603.2 kJ

If the tree absorbed all of that heat, then we use the following equation

change in energy = mass x specific heat capacity x change in temperature

So (be careful of units for energy):

1603200 J = 200 kg x 3.34 x10^3 J/kg-C x change in temperature

The change in temperature is 2.4 C.