9 junio, 2024

Thermal expansion: concept, types, examples, exercises

We explain what thermal expansion is, the types that exist, and we give several examples

What is thermal expansion?

The thermal expansion or thermal expansion is the increase in the dimensions of bodies when they are heated. It happens with almost all materials, except for some that expand when they freeze, like water and acetic acid, for example.

The explanation of the phenomenon lies in the thermal agitation of the particles. According to the kinetic theory, the molecules that make up substances are not at rest, but in permanent motion.

In solids, the particles oscillate around a fixed point, but as the temperature increases, the amplitude of the oscillation increases, and as a consequence the object expands.

This property of materials to expand with temperature is used in many applications, for example in liquid thermometers and bimetallic strips, these bend in a certain way when the temperature increases and in this way circuits can be opened or closed at convenience.

However, sometimes thermal expansion causes drawbacks, as in the case of resins used to treat dental cavities. These resins expand with heat more quickly than teeth, causing discomfort when hot drinks are ingested.

If thermal expansion is not taken into account when designing, the part or object may lose functionality when the temperature rises for some reason.

Types of thermal expansion

Most materials expand when heated, but a few do just the opposite, so there are basically two types of thermal expansion:

The most frequent, which occurs when the material increases simply its dimensions with temperature and is called dilatation either Thermal expansion.
negative thermal expansionif the substance shrinks when heated.

According to the predominant dimensions in the object, the thermal expansion can be linear, superficial or volumetric. For example, if you have a thin wire or bar, the object is elongated and the expansion is linear, since primarily the length is modified.

On the other hand, when a thin sheet is heated, what increases its surface area, while a three-dimensional object increases its volume. For each of these cases there is a simple equation that holds over a good temperature range.

1. Linear dilation

The change in length of a thin rod, bar, or wire is denoted as ΔL and is directly proportional to the change in temperature ΔT and to the original length Lo:

ΔL = α⋅LoΔT

Where:

ΔL = Final length — Initial length = Lf – It
ΔT = Final temperature — Initial temperature = TF — To
α is the constant of proportionality, called coefficient of linear expansion positive if the length increases with temperature.

The values ​​of α for the different substances, in inverse temperature units, are tabulated, almost always at 20 ºC, although the value remains constant over a good range of temperatures.

The above equation can be rewritten to directly calculate the final length:

If = Lo + αLoΔT = Lo(1 + αΔT)

2. Superficial expansion

Analogously to the previous equation, for a shell with initial surface So it can be shown that the new surface Sf is given by:

Sf = So + 2αSo ΔT

3. Volumetric expansion

Finally, for an object of initial volume Vo the new volume Vf is:

Vf = Vo + 3α Vo ΔT

Examples of thermal expansion

hot air in a balloon

When the air inside a balloon is heated, it inflates, since the gas inside expands due to the increase in temperature. It is easily checked by covering a glass bottle with a deflated balloon, which is submerged in hot water. Soon the balloon is seen to begin to inflate.

Expansion joints on sidewalks and roads

In the construction of sidewalks and transit roads, a margin is left for expansion joints, consisting of a separation between the slabs so that, when the temperature rises, they do not crack.

On concrete highways and bridges, spaces are left that are filled with flexible material or with expansion joints in the form of teeth that engage with each other, leaving spaces. This leaves a margin for the concrete to expand and contract with changes in temperature.

glass fractures

Glass cracks under sudden changes in temperature. If a cold glass beaker is filled with very hot water, the material heats unevenly, causing it to expand in places, causing internal stresses that lead to fractures.

Contrary to popular belief, thick glass cracks more easily than thin glass. This is because the thinner the material, the faster and more evenly the heat is distributed, so there is no time for internal stresses to appear.

Freezing of the water

Water is an example of negative thermal expansion, that is, it expands when it cools, a phenomenon that occurs between 0 and 4 ºC. As is known, freezing a fully filled water bottle will cause it to crack.

However, this quality of water makes it possible for the bottom of rivers and lakes not to freeze completely during winter, thus making aquatic life possible even at low temperatures.

power lines

The power lines are not placed in a straight line between two poles, but leaving some margin so that they hang down a bit, forming a curve. It is because, when the weather gets very cold, the wiring tends to shrink.

On the other hand, when the weather is very hot, it is common to see that the power lines relax and hang down a lot.

aircraft rivets

In airplanes, rivets made of aluminum are used to join the pieces, and they are always made larger than the corresponding hole. Then, before putting them in place, they must be contracted, cooling them with dry ice.

There are many reasons why one time weld rivets are preferred for aircraft. For example, the type of aluminum used in the manufacture of airplanes is difficult to weld and even if it is achieved, the welding ends up weakening the material. On the other hand, rivets are easier to inspect and repair than welds.

solved exercise

A thin rod made of bronze is 0.5 m long at 20.0°C. Calculate the length of the rod when it is heated up to 50.0 ºC, knowing that the coefficient of linear expansion of bronze at 20 ºC is: 19 × 10-6 ºC-1 .

Solution

Since the bar is thin, apply the equation for linear expansion:

If = Lo (1 + αΔT)

Simply substitute the values ​​that appear in the statement:

ΔT = (50.0 −20.0) ºC = 30.0 ºC

Lf = 0.5 (1 + 19 × 10-6 × 30) m = 0.500285 m

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