 This is a video for thermal expansion equations as used in physics. For linear expansion, we have this basic equation that you'll see in most textbooks. Reading it math-wise, that's delta L equals alpha L not delta T. But we really want to break that down and see what each of those symbols means. So the first two that we're going to look at are the ones that have the L's in them, the delta L and the L not. Our delta L is the change in length. Most times in physics, that delta means change in. And you can calculate that by using the final length minus the initial length. The L not is the original length or the initial length. And some textbooks might use an L sub i for that as well. Both of these are a measurement of length. So the standard metric unit is going to be meters. But we can actually use any acceptable lengths. So for example, if you had the original length in feet, when you calculate everything, you'll get the change in length in feet. As long as you're consistent between those two, it should be just fine. Next variable we'll look at is delta T. Again, the delta is the change in. So this is the change in temperature, which would be the final temperature minus the initial temperature. And make sure that you realize that this could be positive or negative. The standard metric unit of kelvin is what we use for temperature. But it turns out the change in temperature in kelvin is exactly the same value as the change in temperature in Celsius. So Celsius values for the temperature can be used as well. Our last one is this alpha, the linear expansion coefficient. And that alpha depends on what type of material I have and describes how that particular material relates to changes in temperature. How does it react? So most the time you figure out what material you've got, go to your tables, find that material, look up your alpha value, and that's the value that you're going to use. When we're doing this, we realize that the units we're going to have here are 1 over degrees Celsius, because most of the tables represented that way. But 1 over degrees Celsius is the same as 1 over degrees kelvin when we're talking about a temperature change. So putting this all together, we can come back to our original equation and put this into words. Instead of just saying delta L, we say the change in length of a solid material when heated or cooled is equal to the linear expansion coefficient for that material, multiplied by the original length, multiplied by the change in temperature. The next equation that we're going to take a look at is the volume expansion equation. You'll notice it's very, very similar to the linear expansion. In this case, however, we're doing a change in volume and the original volume. And those are going to have our metric units of meters cubed. Sometimes we're going to run into liters, gallons, other things. Again, as long as you've got the same volume for the V0 and for the delta V, you're going to be OK in your equations. Delta T is exactly the same between these two equations, the change in temperature. Our beta is now the volume expansion coefficient. And again, it's in tables, and it's generally for both solids and liquids. Sometimes for the solids, they won't list the beta value, but in that case, beta is 3 times alpha. And you'll see that in some other references as well. And again, the same basic units. So putting it all together, our volume expansion equation can be expressed as the change in volume of a solid or liquid when heated or cooled is equal to the volume expansion coefficient for that material multiplied by the original volume multiplied by the change in temperature.