In this lesson, you will learn what thermal expansion is and discover an equation for calculating how much different materials expand. You’ll look at a number of examples of thermal expansion. A short quiz will follow.

## What is Thermal Expansion?

One day you’re trying to open a pickle jar, but the lid is super tight and you just can’t do it. You try using a rubber grip, but that doesn’t work. You try hitting the jar lid on the counter to break the seal, but nothing happens. Finally, you try your grandma’s favorite trick: you run the metal jar lid under hot water to heat it up.

The jar opens easily. But why? The answer is thermal expansion.**Thermal expansion** occurs when an object expands and becomes larger due to a change in the object’s temperature. To understand how this happens, we need to think about what temperature actually is.

**Temperature** is the average kinetic (or movement) energy of the molecules in a substance. A higher temperature means that the molecules are moving faster on average. If you heat up a material, the molecules move faster and, as a result, they take up more space – they tend to move into areas that were previously empty. This causes the size of the object to increase.So when you heat up the jar lid, the same thing happens – the jar lid expands. So does the glass, but metals expand more than glass. The gaps between the metal jar lid and the glass threads increase, so it becomes easier to open.

## Equation

This equation describes a linear thermal expansion, which we’ll examine in the context of a metal bar expanding and increasing its length:

In this equation, delta L is the change in length of the bar, delta T is the change in temperature of the bar, L is the original length before the temperature changed, and alpha is the linear coefficient of thermal expansion. The coefficient is just a number that represents how much the material expands. Metals, for example, tend to expand more than plastics.

## Example

We’ve already talked about opening a stubborn jar, but another example of thermal expansion is the joints of a bridge. Bridges are built out of concrete and other relatively firm materials, but these materials expand just like anything else.

When that happens, a bridge could break and collapse. To avoid this, expansion joints are placed on large bridges. That way, as the temperature varies over the course of the year, the bridge is free to get longer or shorter, without causing cracks or breakages.So let’s say a bridge has a length of 50 meters on a day where the temperature is 15 degrees Celsius, and the expansion coefficient of the bridge is 0.0005. How long will the bridge be on a day where the temperature is 35 degrees Celsius?Well, that’s a temperature change of 20 degrees (35 – 15 = 20), so delta T is 20. And, we know both the original length and the expansion coefficient.

So, all we have to do is plug in the three numbers and solve. The change in length will be equal to:0.0005 * 50 * 20 = 0.5 metersSince the bridge is expanding, this means it will have reached a total length of:50.5 meters (50 + 0.5)If you apply this equation in three separate dimensions, you can derive an equation for area expansion or even full 3D volume expansion.

## Lesson Summary

**Thermal expansion** is where an object expands and becomes larger due to a change in its temperature.

A higher temperature means that the molecules are moving faster on average, causing them to take up more space. Consequently, objects that are heated up increase in size.The change in length of an object can be calculated using this equation:

Remember that the linear coefficient indicates how much a particular material expands, since some materials expand more than others.

## Review of Thermal Expansion

- Thermal expansion occurs when an object expands or gets larger due to an increase in its temperature.
- Thermal expansion occurs because heated molecules move faster and take up more space.
- The effect of thermal expansion on an object can be calculated with the following equation:

## Learning Outcomes

Because you’ve studied lesson’s facts on thermal expansion, you could subesequently discover the ability to:

- Detail the meaning and cause of thermal expansion
- Write the equation for calculating the linear thermal expansion of an object