Question

To help prevent frost damage, 4.00 kg of 0ºC water is sprayed onto a fruit tree.

(a) How much heat transfer occurs as the water freezes?
(b) How much would the temperature of the 200-kg tree decrease if this amount of heat transferred from the tree? Take the specific heat to be 3.35 kJ/kg⋅ºC , and assume that no phase change occurs.

Answer 1

a) 1,332 kJ are transferred

b) the temperature of the tree decreases 1.99 ºC

Step-by-step explanation:

a) When a phase change occurs, the temperature remains constant for a pure substance, so, in this case, the heat transferred is:

Q = m*L, where m is the mass, and L is the latent heat, which for solidification of water is -333 kJ/kg:

Q = 4.00*(-333)

Q = -1332 kJ

So, 1,332 kJ are transferred.

b) If the amount of heat is transferred for the tree, and it has no phase change, it will receive a sensitive heat, which is:

Q = m*c*ΔT, where m is the mass, c is the specific heat, and ΔT the temperature change:

-1332 = 200*3.35*ΔT

670ΔT = -1332

ΔT = - 1.99 ºC

So the temperature of the tree decreases 1.99 ºC.