Question

To help prevent frost damage, 4.00 kg of water at 0°C 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·°C, and assume that no phase change occurs in the tree.

a) (a) 1.34 × 10⁵ J, (b) -0.670°C
b) (a) 2.68 × 10⁵ J, (b) -1.34°C
c) (a) 4.01 × 10⁵ J, (b) -2.01°C
d) (a) 5.35 × 10⁵ J, (b) -2.68°C

Answer 1

The total heat transfer when 4.00 kg of water at 0°C freezes is 1.336 × 10⁵ J, and the 200-kg tree's temperature would decrease by approximately 2°C. The correct answer is option (c).

Step-by-step explanation:

Calculation of Heat Transfer During Freezing

To calculate the heat transfer when 4.00 kg of water at 0°C freezes, we use the latent heat of fusion for water. The latent heat of fusion for water is 334 kJ/kg. Therefore, the heat transfer is given by the product of the mass of the water and the latent heat of fusion:

Heat transfer = mass × latent heat of fusion

= 4.00 kg × 334 kJ/kg

= 1336 kJ

Since 1 kJ is equal to 1000 J, this is:

= 1336 kJ × 1000 J/kJ

= 1.336 × 10⁵ J

Temperature Decrease of the Tree

If this heat transfers from the 200-kg tree, we can calculate the decrease in the tree's temperature using the specific heat formula. The specific heat of the tree is given as 3.35 kJ/kg·°C. The temperature change (ΔT) is calculated as follows:

ΔT = Heat transfer / (mass of tree × specific heat)

ΔT = 1336 kJ / (200 kg × 3.35 kJ/kg·°C)

= 2 kJ/kg·°C

The temperature of the tree would decrease by approximately 2°C.

The Correct Answer

Based on these calculations, the correct option for the heat transfer as the water freezes is (c) 4.01 × 10⁵ J, and the correct option for the temperature decrease of the tree is (c) -2.01°C. Therefore, the correct answer for the question is option (c).