Question

100g of water at 25°C is poured into an insulating cup. 50g of ice at 0°C is added to the water. The water is stirred until the temperature of the water has fallen to 0°C.
18g of ice remains unmelted.
The specific heat capacity of water is 4.2J /g 'C. Which value does this experiment give for the specific latent heat of fusion of ice?
A 210J/g
B 330 J /g
C 580 J /g
D 770J/g

Hey, the answer is B, but how? Thanks in advance!

Answer 1

Answer:

330

Explanation:

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Answer 2

Answer:

Concept:

Science Experiment

The latent heat of fusion of ice is 33600 J/K. Latent heat of fusion of ice is the amount of heat required to melt a unit mass of ice from the solid state to the liquid state.

Explanation:

Given:

100g of water at 25°C is poured into an insulating cup.

50g of ice at 0°C is added to the water.

The water is stirred until the temperature of the water has fallen to 0°C.

18g of ice remains unmelted.

The specific heat capacity of water is 4.2J /g 'C.

Find:

Which value does this experiment give for the specific latent heat of fusion of ice

Solution:

Mass of the water,$m_{w}=100 \mathrm{~g}$

The initial temperature of the water, $T_{1 w}=25^{0} \mathrm{C}$

The final temperature of the water, $T_{2 w}=0^{0} \mathrm{C}$

The initial mass of ice,$m_{1}=50 \mathrm{~g}$

The final mass of ice, $m_{2}=18 \mathrm{~g}$

Amount of ice melted, $\Delta m=50-18=32 \mathrm{~g}$

Let $\mathrm{L}$ be the latent heat of fusion of ice,

Heat lost by water = heat gained by ice to melt  $32 \mathrm{~g}$

       

                          $\begin{aligned}m_{w} C \Delta T &=\Delta m L \\& \Rightarrow L=\frac{100 \times 4.2 \times 25}{32} \\& L=328 \mathrm{~J} / \mathrm{g} \approx 330 \mathrm{~J} / \mathrm{g}\end{aligned}$

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