Thermodynamics question regarding latent heat of fusion of ice.

In summary, the problem involves an insulated copper container with 0.350 kg of water initially at 25.0 0C, and 0.012 kg of ice at 0.0 0C is added. The container and contents reach thermal equilibrium at 21.7 0C. The total heat released as the copper and water cool down is 5154.104J. To determine the latent heat of fusion of ice, the heat lost by the copper and water must be taken into account. Using the equations Q=mc delta T and Q=mL, the heat lost by the copper and water can be calculated and rearranged to find the latent heat of fusion of ice.
  • #1
Bigdutchman
2
0

Homework Statement


(a) An insulated copper container of mass 0.250 kg contains 0.350 kg water. Both the container and the water are initially at 25.0 0C. Then 0.012 kg of ice at 0.0 0C is added to the container. Eventually the container and contents reach thermal equilibrium at 21.7 0C.

(i) What is the total heat released (in J) by the copper container and the 0.350 kg water as they cool down from 25.0 0C to 21.7 0C?

I got 5154.104J (Correct answer)


(ii) Determine the latent heat of fusion of ice. <---- Can't do this mofo. Keep getting different answer. They have 3.39x10^5 J/kg. Can someone pls show me how they got that? THANKS!



Homework Equations


Q=mc delta T
Q=mL


The Attempt at a Solution


One of my failed attempts:
5154/0.012 = 4.29x10^5 J/kg
 
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  • #2
You are not taking into account the heat lost by the copper and the water.

AM
 
  • #3
how do i do that? lol
 
  • #4
Bigdutchman said:
how do i do that? lol
If the copper changes temperature by [itex]\Delta T[/itex] how much heat does it lose? Do the same for water.

AM
 
  • #5
Q = mL for state changes. (mass, L being the heat needed, which is what you're trying to find)

and for heating of liquids, Q = mC * change in temp

heat lost by copper = -heat lost by water (i.e. heat is gained by water)
mC * change in temp for copper = - (mL + mC * change in temp for water)

rearrange to find L
 

FAQ: Thermodynamics question regarding latent heat of fusion of ice.

1. What is latent heat of fusion of ice?

The latent heat of fusion of ice is the amount of heat required to change a unit mass of ice from solid to liquid state at constant temperature and pressure. It is a characteristic property of a substance and is also known as the heat of fusion.

2. How is latent heat of fusion of ice measured?

The latent heat of fusion of ice is measured by using a calorimeter, which is a device that can accurately measure the amount of heat released or absorbed during a physical or chemical change. The process involves melting a known mass of ice and measuring the amount of heat required to do so.

3. Why does ice require a specific amount of heat to melt?

Ice requires a specific amount of heat to melt because it undergoes a phase change from solid to liquid. During this phase change, the molecular structure of ice changes and energy is required to break the intermolecular bonds holding the molecules together. This energy is known as the latent heat of fusion.

4. How does latent heat of fusion affect the melting and freezing of ice?

The latent heat of fusion plays a crucial role in the melting and freezing of ice. When heat is applied to ice, it first increases the temperature of the ice until it reaches its melting point. At this point, the heat energy is used to break the bonds between the ice molecules, causing it to melt. On the other hand, when heat is removed from liquid water, it first cools down until it reaches its freezing point. At this point, the heat energy is released as the water molecules form bonds and turn into ice.

5. How does the latent heat of fusion of ice relate to thermodynamics?

The latent heat of fusion of ice is a fundamental concept in thermodynamics as it describes the transfer of energy during a phase change. Thermodynamics deals with the relationships between heat, work, and energy, and the latent heat of fusion is an important factor in these relationships. It is also used in various thermodynamic processes, such as refrigeration and air conditioning, where the phase change of substances is involved.

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