Modern Physics

Thermal Expansion: Coefficient, Types and Exercises

The thermal expansion is increased or variations of various metric dimensions (such as length or volume) which is subjected to a physical object or body. This process occurs due to the increase in temperature around the material. In the case of linear expansion, these changes occur in a single dimension.

The coefficient of this expansion can be measured by comparing the magnitude value before and after the process. Some materials experience the opposite of thermal expansion; that is, it becomes “negative”. This concept proposes that some materials contract when exposed to certain temperatures.

Thermal expansion in water

For solids, a coefficient of linear expansion is used to describe their expansion. On the other hand, a volumetric expansion coefficient is used for liquids to perform the calculations.

In the case of crystallized solids, if it is isometric, the expansion will be general in all dimensions of the crystal. If it is not isometric, different coefficients of expansion can be found along the glass and it will change size as the temperature changes.

Thermal expansion coefficient

The coefficient of thermal expansion (Y) is defined as the radius of change that a material has undergone due to the change in temperature. This coefficient is represented by the symbol α for solids and β for liquids and is guided by the International System of Units.

Thermal expansion coefficients vary when dealing with solids, liquids or gases. Each has a different quirk.

For example, the expansion of a solid can be seen along a length. The volumetric coefficient is one of the most basic in terms of fluids and changes are visible in all directions; This coefficient is also used in calculating the expansion of a gas.

negative thermal expansion

Negative thermal expansion occurs in some materials that, instead of increasing in size with high temperatures, shrink due to low temperatures.

This type of thermal expansion is usually observed in open systems, where directional interactions are observed – as in the case of ice – or in complex compounds – as in some zeolites, Cu2O, among others.

Furthermore, some research has shown that negative thermal expansion also occurs in one-component networks, in a compact form and with a central force interaction.

A clear example of negative thermal expansion can be seen when adding ice to a glass of water. In this case, the high temperature of the liquid in the ice does not cause it to increase in size, but its size is reduced.


When calculating the expansion of a physical object, it should be taken into account that, depending on the change in temperature, that object can grow or shrink in size.

Some objects do not require a drastic temperature change to change their size, so the value shown by the calculations will likely be average.

Like any process, thermal expansion is divided into several types that explain each phenomenon separately. For solids, the types of thermal expansion are linear expansion, volumetric expansion, and surface expansion.

linear dilation

In linear expansion, a single variation predominates. In this case, the only unit that changes is the height or width of the object.

An easy way to calculate this type of expansion is to compare the magnitude value before the temperature change with the magnitude value after the temperature change.

surface or area dilation

In the case of superficial dilation, an increase in the area of ​​a body or object is observed as there is a change in temperature at 1°C.

This expansion works for solids. If you also have the linear coefficient, you can see that the object’s size will be 2 times larger. The formula to calculate it is:

f = A[1 + YA (T f – T )]

In this expression:

γ = area expansion coefficient [° C -1 ]

THE = initial area

f = final area

T = initial temperature.

f = final temperature

The difference between area dilation and linear dilation is that in the first you see an increase change in the area of ​​the object, and in the second the change is of a single unit of measurement (such as the length or width of the physical object).


First exercise (linear dilation)

The tracks that make up a steel train track are 1500 m long. What will be the length when the temperature goes from 24 to 45 °C?



LO (initial length) = 1500 m

f (final length) =?

A (initial temperature) = 24 °C

f (final temperature) = 45 °C

α (coefficient of linear expansion corresponding to steel) = 11 x 10 -6 ° C -1

The data is replaced in the following formula:

Thermal Expansion: Coefficient, Types and Exercises 3

However, you must first know the temperature differential value in order to include this data in the equation. To achieve this differential, the highest temperature must be subtracted from the lowest.

Δt = 45°C – 24°C = 21°C

Once this data is known, you can use the formula above:

Lf = 1500 m (1 + 21 ° C. 11 x 10 -6 ° C -1 )

Lf = 1500 m (1 + 2.31 x 10 -4 )

Lf = 1500 m (1,000231)

Lf = 1500.3465 m

Second exercise (superficial dilation)

In a prep school, a glass sale has an area of ​​1.4 m^2 if the temperature is 21°C. What will your final area be by increasing the temperature to 35°C?


Af = A0 [1 + (Tf – T0)]

Af = 1.4 m 2 [1] 204.4 x 10 -6 ]

Af = 1.4 m 2 . 1.0002044

Af = 1.40028616 m 2

Why does the dilation happen?

Everyone knows that every material is made up of many subatomic particles. By changing the temperature, increasing or decreasing, these atoms start a process of movement that can change the shape of the object.

When the temperature increases, molecules start to move quickly due to the increase in kinetic energy and therefore the shape or volume of the object increases.

In the case of negative temperatures, the opposite happens; in this case, the object’s volume is usually contracted by low temperatures.

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