Basic Physics

# Linear expansion

Most solid objects experience a linear expansion when the temperature changes. The linear expansion is the length of the object increases or the length of the object decreases. Usually, the length of the object increases when the temperature increases, whereas the length of the object decreases when the temperature drops. You might think that linear expansion can only occur on objects such as thin wires. For example, look at a car that is parked on the side of the road, so it is exposed to the sun. When the car overheats, the iron plate can get thicker, or the side length can increase. Roofs of houses made of zinc can also experience expansion. In this case, when zinc is overheated, the edges of zinc increase in width and zinc can even get thicker. The same thing happened to the railroad tracks and iron or steel on the bridge.

Most solid objects expand or shrink when the temperature of the object changes, so we need to know how the temperature changes affect to the expansion of solid objects. For example, a gap in the railroad tracks. Railroad tracks are made of steel. The engineers had calculated the width of the gap between each rail. On a hot day, the rail will expand a few centimeters. When passed by a train, the rail temperature also increases so that the rail extends for how many centimeters. On cold nights, the rails shrink to how many centimeters.

Based on the results of the analysis, the engineers estimate the distance between the rail gap, so that when the rail temperature increases, the rail does not touch each other and becomes bent.

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To help us derive a formula that states the relationship between temperature changes and the magnitude of length expansion, review a solid object experiencing expansion, as shown in the figure below.

To = initial temperature, T = final temperature, Lo = initial length, ΔL = change in length, L = length after expansion, ΔT = change in temperature.

When object temperature = To (object is still cold), object length = Lo. When the temperature of the object = T (the temperature of the object increases), the length of the object = L. Based on the results of observations and experiments, the changes in the length of the object are proportional to the changes in temperature. If the temperature increases, the length of the object increases. Conversely, when the temperature decreases, the length of the object decreases. The change in length of an object is also proportional to the length of the original object (Lo). If the temperature changes are the same, objects that are 10 meters long, for example, will be doubled in length compared to objects that are only 5 meters long. So the longer the object, the greater the expansion of the object.

Changes in object length ((L) are proportional to changes in temperature (ΔT): ΔL α ΔT

Changes in the length of an object (ΔL) are proportional to the length of the original object (Lo): ΔL α Lo

Changes in the length of each object vary. Although the temperature changes are the same, the expansion experienced by iron is not the same as glass. Likewise with other objects. So the linear expansion depends on the coefficient of linear expansion of each object. The greater the coefficient of linear expansion, the greater the length increase. The smaller the coefficient of linear expansion, the smaller the length increase. It could be said that the change in length of an object is proportional to the coefficient of linear expansion.

L ∝ α

The three comparisons above are expressed in an equation:

Description: ΔL = The change in length, α = The coefficient of linear expansion (units α = K-1 or (Co)-1, Lo = Initial length, ΔT (T1 – To) ΔT = The changes in temperature (final temperature – initial temperature )

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The total length of an object after experiencing expansion or shrinkage can be obtained by adding the initial length of the object (Lo) and the change in length of the object (ΔL).

Description: ΔL = length of the object after expanding or shrinking, Lo = The initial length of the object, ΔL = L – Lo = The change in length, α = The cooficient of linear expansion (units of α = K-1 or (Co)-1, ΔT = T – To = Temperature change, To = The initial temperature, T = the final temperature.

If the temperature change (T-To) is negative, then the change in length (L-Lo) is also negative.

In this case, the length of the object decreases. Conversely, if the temperature change (T-To) is positive, then the change in length (L-Lo) is also positive. In this case objects increase in length.

Following is the value of the coefficient of linear expansion of the solid objects, at a temperature of 20 °C. The shape of the liquid and gas substances changes so that these two types of substances cannot experience the linear expansion. The coefficient of linear expansion of a solid object also depends on temperature. At different temperatures, the coefficient of linear expansion of solid objects also varies. If the temperature difference is not too significant, the difference in the coefficient of linear expansion is not too significant so that it can be ignored.

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