10.3.3. Latent Heat of Fusion

Latent heat is the heat required to change the state of a substance without changing its temperature. There are two main types of latent heat:

• Latent Heat of Fusion: The heat required to change a substance from solid to liquid at constant temperature (e.g., ice melting to water).
• Latent Heat of Vaporization: The heat required to change a substance from liquid to gas at constant temperature (e.g., water boiling to steam).

Latent heat refers to the energy needed to change a substance from one state to another without altering its temperature. When we talk about states, we mean solid, liquid, and gas. The two primary types of latent heat are:

1. Latent Heat of Fusion: This is the energy required to change a solid into a liquid. A classic example is when ice melts into water. Even though heat is added to the ice (causing it to melt), the temperature remains constant while this change occurs.

2. Latent Heat of Vaporization: This refers to the energy needed to change a liquid into a gas, like when water boils and turns into steam. Again, during this process, the temperature stays the same until the entire liquid has changed to gas.

Think of ice cubes in a drink. When you add heat from the drink to the ice, it melts and becomes water, but the temperature of the ice doesn't rise above 0°C until all of it has melted. This is because the heat energy is being used to change the state of the ice to water, demonstrating latent heat of fusion.

The formula for calculating the heat required for a phase change is:

Q = mL

Where:

• Q = Heat energy (in Joules)
• m = Mass of the substance (in kilograms)
• L = Latent heat of fusion or vaporization (in J/kg)

The formula for calculating the heat needed for a phase change is fairly straightforward. It’s expressed as:

• Q = mL
  • Q is the heat energy that is transferred, measured in Joules.
  • m is the mass of the substance undergoing the phase change, measured in kilograms.
  • L is the latent heat of the specific phase change (fusion or vaporization), represented in Joules per kilogram.

This formula allows us to determine how much heat is needed depending on the mass of the substance and which phase change is occurring.

Consider making ice cream at home. If you want to completely melt a certain mass of ice (say, 1 kg) to make the desired treat, you can use this formula to calculate how much heat is required based on the latent heat of fusion (334 kJ). The more ice you have, the more heat is necessary to melt it, as represented by the mass in the formula.

To melt 500 grams of ice at 0°C, using the latent heat of fusion:

Q = 0.5 × 334 = 167 kJ

Hence, 167 kJ of heat is required to melt 500 grams of ice.

Here's how the calculation works in practice:

Suppose we need to melt 500 grams (which is 0.5 kg) of ice at 0°C. We know that the latent heat of fusion for ice is 334 kJ/kg. Using the formula Q = mL:

1. First, convert grams to kilograms (500 g = 0.5 kg).
2. Then, plug in the numbers: Q = 0.5 kg × 334 kJ/kg.
3. Calculate to find that Q = 167 kJ.

This means that you need 167 kJ of heat energy to completely melt 500 grams of ice, ensuring it turns to water without a temperature rise during the process.

Imagine making a refreshing summer drink with a lot of ice. When you pour warm lemonade over the ice, the ice absorbs heat to melt into water. You can think of the 167 kJ of heat as the energy needed not only for the ice to change form but also to keep your drink chilled at the perfect temperature!

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