Latent Heat of Fusion

The latent heat of fusion is the energy required to change a substance from a solid to a liquid at its melting point. It is also known as the heat of liquefaction. The latent heat of fusion is a measure of the strength of the intermolecular forces in a substance. The stronger the intermolecular forces, the more energy is required to break them and melt the substance.

Formula for Latent Heat of Fusion

The latent heat of fusion is typically denoted by the symbol $L_f$. The formula for the latent heat of fusion is:

$$L_f = \frac{Q}{m}$$

where:

• $L_f$ is the latent heat of fusion in joules per kilogram (J/kg)
• $Q$ is the energy required to melt the substance in joules (J)
• $m$ is the mass of the substance in kilograms (kg)

Units of Latent Heat of Fusion

The SI unit of latent heat of fusion is joules per kilogram (J/kg). However, other units such as calories per gram (cal/g) and British thermal units per pound (Btu/lb) are also commonly used.

Factors Affecting Latent Heat of Fusion

The latent heat of fusion of a substance depends on several factors, including:

• Intermolecular forces: The stronger the intermolecular forces, the higher the latent heat of fusion.
• Molecular weight: The heavier the molecules of a substance, the higher the latent heat of fusion.
• Crystal structure: The more ordered the crystal structure of a substance, the higher the latent heat of fusion.

Examples of Latent Heat of Fusion

The following table lists the latent heat of fusion for some common substances:

Substance	Latent Heat of Fusion (J/kg)
Water	333,500
Ice	333,500
Aluminum	397,000
Copper	205,000
Gold	63,000

Specific Latent Heat of Fusion

The specific latent heat of fusion is the amount of energy required to change one gram of a substance from a solid to a liquid at its melting point. It is measured in joules per gram (J/g).

The specific latent heat of fusion is a characteristic property of a substance. It is constant for a given substance at its melting point.

The specific latent heat of fusion can be used to calculate the amount of energy required to melt a given mass of a substance. The formula is:

$$Q = mL$$

where:

• Q is the amount of energy required (in joules)
• m is the mass of the substance (in grams)
• L is the specific latent heat of fusion (in J/g)

Example

Calculate the amount of energy required to melt 100 grams of ice at 0°C.

The specific latent heat of fusion of ice is 334 J/g.

$$Q = mL = (100 g)(334 J/g) = 33,400 J$$

Therefore, 33,400 joules of energy are required to melt 100 grams of ice at 0°C.

Latent Heat of Fusion Formula

The latent heat of fusion is the energy required to change a substance from a solid to a liquid at its melting point, or from a liquid to a solid at its freezing point. It is typically measured in joules per gram (J/g) or kilojoules per mole (kJ/mol).

Formula

The latent heat of fusion can be calculated using the following formula:

$$L = Q / m$$

where:

• L is the latent heat of fusion (J/g or kJ/mol)
• Q is the energy required to change the phase of the substance (J or kJ)
• m is the mass of the substance (g or mol)

Example

For example, the latent heat of fusion of water is 334 J/g. This means that it takes 334 joules of energy to melt one gram of ice at 0°C.

The latent heat of fusion is an important property of materials that has many applications. By understanding the latent heat of fusion, we can better understand how materials behave and how they can be used to our advantage.

Applications of Latent Heat of Fusion

Latent heat of fusion is the energy required to change a substance from a solid to a liquid at its melting point, or from a liquid to a solid at its freezing point. This energy is absorbed or released without a change in temperature.

The latent heat of fusion has many important applications in everyday life and industry. Some of the most common applications include:

1. Heating and Cooling

• Thermal Energy Storage: Latent heat of fusion is used in thermal energy storage systems to store thermal energy for later use. For example, some solar thermal systems use phase change materials (PCMs) to store excess heat from the sun during the day, which can then be released at night to heat a building.
• Refrigeration: Latent heat of fusion is used in refrigerators and freezers to keep food cold. The refrigerant absorbs heat from the food, causing it to melt. The refrigerant then releases this heat when it condenses back into a liquid, keeping the food cold.

2. Food Processing

• Freezing and Thawing: Latent heat of fusion is used to freeze and thaw food. When food is frozen, the water in the food turns to ice, releasing latent heat. This heat helps to preserve the food by slowing down the growth of bacteria. When food is thawed, the ice melts, absorbing latent heat. This heat helps to bring the food back to a safe temperature for consumption.
• Dehydration: Latent heat of fusion is used to dehydrate food. When food is dehydrated, the water in the food is removed, causing it to lose weight and volume. This process can help to preserve food by preventing the growth of bacteria.

3. Metalworking

• Casting: Latent heat of fusion is used in metalworking to cast metals. When metal is melted, it absorbs latent heat. This heat helps to keep the metal molten so that it can be poured into a mold. When the metal cools and solidifies, it releases latent heat. This heat helps to ensure that the metal casting is solid and free of defects.
• Welding: Latent heat of fusion is used in welding to join two pieces of metal together. When the metal is heated, it melts and fuses together. When the metal cools and solidifies, it releases latent heat. This heat helps to create a strong bond between the two pieces of metal.

4. Pharmaceuticals

• Drug Delivery: Latent heat of fusion is used in drug delivery systems to control the release of drugs. Some drugs are encapsulated in a material that has a high latent heat of fusion. When the material is heated, it melts and releases the drug. This allows for a controlled release of the drug over time.

5. Other Applications

• Ice Skating Rinks: Latent heat of fusion is used to create ice skating rinks. Water is frozen on a surface, and the latent heat released by the water helps to keep the ice cold.
• Snowmaking: Latent heat of fusion is used to make snow. Water is sprayed into the air, and the latent heat released by the water helps to freeze the water into snow.
• Thermal Protection: Latent heat of fusion is used in thermal protection systems to protect objects from extreme temperatures. For example, some spacecraft are equipped with heat shields that use latent heat of fusion to absorb heat from the sun.

The latent heat of fusion is a powerful tool that has many important applications in everyday life and industry. By understanding the latent heat of fusion, we can design and develop new technologies that can improve our lives and make the world a better place.

Solved Examples on Latent Heat of Fusion

Example 1: Melting Ice

A 100-gram ice cube at 0°C is placed in a pot of boiling water. How much heat is required to melt the ice cube and raise its temperature to 100°C?

Solution:

The heat required to melt the ice cube can be calculated using the formula:

$$Q = mL$$

where:

• Q is the heat required (in joules)
• m is the mass of the ice cube (in kilograms)
• L is the latent heat of fusion of ice (334 kJ/kg)

Substituting the given values into the formula, we get:

$$Q = (0.1 kg)(334 kJ/kg) = 33.4 kJ$$

Therefore, 33.4 kJ of heat is required to melt the ice cube.

To raise the temperature of the melted ice cube from 0°C to 100°C, we can use the formula:

$$Q = mc_p\Delta T$$

where:

• Q is the heat required (in joules)
• m is the mass of the water (in kilograms)
• c$_p$ is the specific heat capacity of water (4.18 kJ/kg°C)
• ΔT is the change in temperature (in °C)

Substituting the given values into the formula, we get:

$$Q = (0.1 kg)(4.18 kJ/kg°C)(100°C) = 41.8 kJ$$

Therefore, 41.8 kJ of heat is required to raise the temperature of the melted ice cube from 0°C to 100°C.

The total heat required to melt the ice cube and raise its temperature to 100°C is:

$$Q_{total} = Q_{melting} + Q_{raising temperature}$$

$$Q_{total} = 33.4 kJ + 41.8 kJ = 75.2 kJ$$

Therefore, 75.2 kJ of heat is required to melt the ice cube and raise its temperature to 100°C.

Example 2: Freezing Water

A 100-gram sample of water at 100°C is placed in a freezer at -18°C. How much heat is released when the water freezes and cools to -18°C?

Solution:

The heat released when the water freezes can be calculated using the formula:

$$Q = mL$$

where:

• Q is the heat released (in joules)
• m is the mass of the water (in kilograms)
• L is the latent heat of fusion of water (334 kJ/kg)

Substituting the given values into the formula, we get:

$$Q = (0.1 kg)(334 kJ/kg) = 33.4 kJ$$

Therefore, 33.4 kJ of heat is released when the water freezes.

To cool the frozen water from 0°C to -18°C, we can use the formula:

$$Q = mc_p\Delta T$$

where:

• Q is the heat released (in joules)
• m is the mass of the water (in kilograms)
• c_p is the specific heat capacity of ice (2.09 kJ/kg°C)
• ΔT is the change in temperature (in °C)

Substituting the given values into the formula, we get:

$$Q = (0.1 kg)(2.09 kJ/kg°C)(-18°C) = -3.76 kJ$$

Therefore, 3.76 kJ of heat is released when the frozen water cools from 0°C to -18°C.

The total heat released when the water freezes and cools to -18°C is:

$$Q_{total} = Q_{freezing} + Q_{cooling}$$

$$Q_{total} = 33.4 kJ + (-3.76 kJ) = 29.6 kJ$$

Therefore, 29.6 kJ of heat is released when the water freezes and cools to -18°C.

Latent Heat of Fusion FAQs

What is latent heat of fusion?

• Latent heat of fusion is the energy required to change a substance from a solid to a liquid at its melting point, or from a liquid to a solid at its freezing point.
• It is called “latent” because the energy is not used to increase the temperature of the substance, but rather to overcome the intermolecular forces that hold the molecules in place in the solid state.

What is the difference between latent heat of fusion and specific heat capacity?

• Specific heat capacity is the amount of energy required to raise the temperature of a substance by one degree Celsius.
• Latent heat of fusion is the amount of energy required to change the phase of a substance, from solid to liquid or vice versa.

What are some examples of latent heat of fusion?

• The latent heat of fusion of water is 334 kJ/kg. This means that it takes 334 kJ of energy to melt one kilogram of ice at 0°C.
• The latent heat of fusion of aluminum is 397 kJ/kg. This means that it takes 397 kJ of energy to melt one kilogram of aluminum at 660°C.
• The latent heat of fusion of gold is 63 kJ/kg. This means that it takes 63 kJ of energy to melt one kilogram of gold at 1064°C.

How is latent heat of fusion used in everyday life?

• Latent heat of fusion is used in a variety of everyday applications, including:
• Refrigeration: Refrigerators use a compressor to circulate a refrigerant, which undergoes a phase change from a liquid to a gas and back again. This phase change absorbs and releases heat, which is used to cool the inside of the refrigerator.
• Air conditioning: Air conditioners work in a similar way to refrigerators, using a refrigerant to cool the air.
• Heating: Some heating systems use a phase change material (PCM) to store heat. The PCM melts during the day, absorbing heat from the sun, and then releases the heat at night, when the temperature drops.
• Thermal energy storage: Latent heat of fusion can be used to store thermal energy for later use. This is done by melting a PCM and then storing it in an insulated container. When the heat is needed, the PCM can be re-solidified, releasing the stored heat.

Conclusion

Latent heat of fusion is an important concept in thermodynamics that has a variety of applications in everyday life. By understanding latent heat of fusion, we can better understand how heat is transferred and stored, and how it can be used to our advantage.