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In this lesson, we will learn how to relate the mass conversion between solid and liquid states to net heating and the latent heat of fusion.

Q1:

Some gun owners make their own bullets, which involves them melting lead and casting it into lead slugs. A 0.198 kg mass of lead at an initial temperature of 7 . 0 0 ∘ C is heated to its melting point temperature of 3 2 7 ∘ C and completely melted. Determine the heating required to do this. Use a value of 1 2 8 / ⋅ J k g C ∘ for the specific heat capacity of lead and use a value of 24.5 kJ/kg for the specific latent heat of fusion of lead.

Q2:

To help prevent frost damage to a fruit tree, 4.00 kg of water at 0 . 0 0 ∘ C is sprayed onto the tree and allowed to freeze. The specific latent heat of fusion of water is 334 kJ/kg.

How much heat transfer occurs as the water freezes?

The tree has a mass of 200 kg and a specific heat capacity of 3 . 3 5 / ⋅ k J k g C ∘ . How much would the temperature of the tree have decreased if it had not been sprayed by water, assuming that no state changes occur in the matter of the tree as it cools?

Q3:

An ice cube has a mass of 5 . 0 0 × 1 0 − 2 kg. The ice cube is placed inside a perfectly insulated container that holds 0.400 kg of water at an initial temperature of 3 5 . 0 ∘ C . Find the final temperature inside the container. Use a value of 4 1 8 2 / ⋅ J k g C ∘ for the specific heat capacity of water and 334 kJ/kg for the specific latent heat of fusion of ice.

Q4:

A bag containing ice at a temperature of 0 ∘ C is much more effective in absorbing energy than a bag containing the same amount of water at a temperature of 0 ∘ C . The specific heat capacity of water is 4 1 8 6 / ⋅ J k g C ∘ and the specific latent heat of fusion of ice is 334 kJ/kg.

How much heat transfer is necessary to raise the temperature of 0.800 kg of water from 0 . 0 ∘ C to 3 0 . 0 ∘ C ?

How much heat transfer is necessary to melt of 0.800 kg of ice at 0 . 0 ∘ C and then increase its temperature to 3 0 . 0 ∘ C ?

Q5:

A 0.800-kg iron cylinder at a temperature of 1 . 0 0 × 1 0 3 ∘ C is dropped into an insulated copper container of mass 1.50 kg, that contains 0.500 kg of ice at its melting point. The container is in thermal equilibrium with the ice. The specific heat capacity of copper is 3 8 7 / ⋅ J k g C ∘ . The specific heat capacity of iron is 4 5 2 / ⋅ J k g C ∘ . The specific latent heat of fusion of ice is 334 kJ/kg.

What is the final temperature of the container and its contents?

Q6:

An iron cylinder has a mass of 0.80 kg and a temperature of 1 . 0 0 × 1 0 3 ∘ C . The cylinder is dropped into an insulated chest containing 1.0 kg of ice at its melting point. What is the equilibrium temperature of the chest’s contents? Use a value of 4 1 8 0 / ⋅ J k g C ∘ for the specific heat capacity of water, a value of 334 kJ/kg for the latent heat of fusion of water, and a value of 4 5 2 / ⋅ J k g C ∘ for the specific heat capacity of iron.

Q7:

In 1986, an enormous iceberg broke away from the Ross Ice Shelf in Antarctica. Assume that the iceberg was a rectangular prism 160 km long, 40.0 km wide, and 250 m thick. Assume a density for the iceberg of 917 kg/m^{3} and a specific latent heat of fusion for the ice of 334 kJ/kg.

What was the iceberg’s mass?

How much heating of the iceberg would be needed to melt it?

How much time would it take sunlight to melt the iceberg? Assume 12.00 h of sunlight per day, with a light intensity of 100 W/m^{2}.

Q8:

An iron cylinder has a mass of 1.20 kg and is at a temperature of 8 6 0 ∘ C . The cylinder is placed inside a perfectly insulated chest that contains 0.70 kg of ice at a temperature of 0 . 0 ∘ C . The iron and ice reach an equilibrium temperature which depends on their thermal properties. Use a value of 4 5 2 / ⋅ J k g C ∘ for the specific heat capacity of iron, a value of 2 0 9 0 / ⋅ J k g C ∘ for the specific heat capacity of ice, a value of 4 1 8 4 / ⋅ J k g C ∘ for the specific heat capacity of water, and a value of 333.55 J/g for the specific latent heat of fusion of water.

What equilibrium temperature is reached?

What mass of ice is melted?

Q9:

An ice cube has a mass of 64.0 g. The ice cube is placed inside an aluminum calorimeter that has a mass of 78.0 g. The calorimeter already contains 583.0 g of an unknown liquid, which the calorimeter is in thermal equilibrium with at a temperature of 2 7 . 0 ∘ C . The equilibrium temperature of the calorimeter and its contents after the ice cube is added is 9 . 0 ∘ C . Determine the specific heat capacity of the unknown liquid. Use a value of 9 0 0 / ⋅ J k g C ∘ for the specific heat capacity of aluminum, a value of 4 1 8 4 / ⋅ J k g C ∘ for the specific heat capacity of water, and a value of 333.55 J/g for the specific latent heat of fusion of water.

Q10:

A bag of ice has a mass of 4.10 kg. The bag of ice is in a cooler that is taken on a picnic. All of the ice melts after 720.000 minutes of picnicking. The ice temperature at the start of the picnic is 0 . 0 0 ∘ C and the water temperature at the end of the picnic is also 0 . 0 0 ∘ C . Determine the average heating power received by the ice. Use a value of 333.55 J/g for the specific latent heat of fusion of water.

Q11:

A package of frozen vegetables has a mass of 0.740 kg and is at a temperature of 0 . 0 0 ∘ C . Determine how much heating of the vegetables is required to thaw them. Use a value of 333.55 J/g for the specific latent heat of fusion of water.

Q12:

A block of ice has a mass of 0.100 kg and an initial temperature of − 2 2 . 0 ∘ C . A 0.100 kg mass of water that has a temperature of 1 7 . 0 ∘ C is poured onto the ice. Determine the equilibrium temperature of the ice and water, assuming that the temperature is reached sufficiently rapidly and that heat loss from the ice and water is negligible. Use a value of 4 1 8 4 / ⋅ J k g C ∘ for the specific heat capacity of water, 2 0 9 0 / ⋅ J k g C ∘ for that of ice, and 333.55 J/kg for the specific latent heat of fusion of water.

Q13:

An aluminum soup bowl has a mass of 0.280 kg. The bowl holds a 0.730 kg mass of soup. The soup and bowl are at an initial temperature of 1 8 . 0 ∘ C before being placed in a freezer. At an instant 𝑡 , the bowl and soup have heated the air in the freezer by 320 kJ, although the temperature in the freezer has remained constant as the heated air is continually cooled by the freezer’s cooling system. Determine the temperature of the bowl and soup at the instant 𝑡 . Use a value of 4 1 8 6 / ⋅ J k g C ∘ for the specific heat capacity of liquid soup, 2 0 9 0 / ⋅ J k g C ∘ for the specific heat capacity of solid soup, 9 0 0 / ⋅ J k g C ∘ for the specific heat capacity of aluminum, and 334 J/g for the specific latent heat of fusion of soup.

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