# Heat of Fusion: Definition, Equation & Examples

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• 0:00 Review of Latent Heat
• 1:46 Latent Heat of Fusion
• 2:45 Problem Solving Example
• 5:33 Lesson Summary

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Lesson Transcript
Instructor: Amy Lange

Amy has taught university-level earth science courses and has a PhD in Geology.

This lesson will examine the heat of fusion, which is the energy required for matter to change between a liquid and a solid. In this lesson, we review the concepts of latent heat and work through a problem using our new understanding of the heat of fusion.

## Review of Latent Heat

The heat of fusion, also known as the latent heat of fusion, is a category of latent heat describing the energy for the phase change between a liquid and a solid to occur without a change in temperature. To fully grasp this concept, let's first review latent heat.

Latent heat is the heat per mass unit required for a phase change to occur. Think about what happens when you add ice and cold soda to a glass. Because the soda is warmer than 0 degrees Celsius, the melting point of ice, we would expect that the heat from the slightly warmer soda to melt the ice in the glass. However, you've probably noticed that when you add ice to an already cold drink, only some of the ice melts, not all of it. This is because the soda does not contain enough energy as heat to overcome the latent heat of fusion of the ice. We'll revisit this problem with some calculations later in the lesson.

When you combine ice at 0 degrees Celsius and cold soda at a temperature above 0 degrees Celsius, the heat from the soda will continue to melt the ice until both reach an equilibrium temperature.

When heat energy is added to or removed from an object, the temperature of the object normally adjusts accordingly. However, during a phase change, the temperature of an object will remain constant despite additional heat being added or subtracted from the substance.

So what's happening to the excess heat during this transfer of energy if it isn't changing the temperature? This heat energy is going toward overcoming the latent heat of the substance.

This graph shows how the temperature of water will vary when heat is added. The blue boxes mark the zones of phase changes. During this time, the energy that is added goes toward overcoming the latent heat of the water, so the temperature does not change until the phase change is complete.

## Latent Heat of Fusion

The three common states of matter are gas, liquid, and solid. Thus, there are three different terms for latent heat describing phase changes between these states of matter. The latent heat of fusion refers to the phase change between solid and liquid. Take note that although 'heat' is often thought as state of being hot, heat actually refers to the transfer of heat energy between objects. Thus, the latent heat of fusion encompasses the process of adding heat to melt a solid and the process of subtracting heat to freeze a liquid.

The latent heat of fusion, noted as L sub f, has the same equation as the general equation for latent heat.

This equation states that the heat Q that must be added or removed for a phase change to occur is proportional to the mass of the substance m times its unique latent heat of fusion, L sub f.

## Problem-Solving Example

Let's return to our soda and ice example and solve how much ice is remaining after combining cold soda and ice. We know that in order for the ice to melt, the ice needs to absorb enough heat energy to overcome the latent heat of fusion. We also know that not all of our ice melts when added to the cold soda, so they must reach an equilibrium temperature of 0 degrees Celsius.

Let's assume our soda and ice are a perfectly isolated system, meaning that it doesn't receive or lose any heat from the glass or its surroundings. So the only source of heat to melt the ice would be the cold soda. As the soda cools down to 0 degrees, some of its heat energy is lost to the ice. How do we calculate how much heat energy is lost?

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