Thermal Dilation: Coefficient, Types And Exercises

The thermal expansion  is increased or variation of various metric dimensions (such as length or volume) that undergoes a physical object or body. This process happens due to the increase in temperature surrounding the material. In the case of linear dilation, these changes occur in only one dimension.

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

Thermal expansion

For solids, a linear expansion coefficient is used to describe their expansion. On the other hand, for liquids a volumetric coefficient of expansion is used 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 throughout the glass, and it will change its size when the temperature changes.

Thermic dilatation coefficient

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

The coefficients of thermal expansion vary when it comes to solid, liquid or gas. Each one has a different peculiarity.

For example, the dilation of a solid can be seen along a length. The volumetric coefficient is one of the most basic in terms of fluids, and the changes are notable in all directions; This coefficient is also used when 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, contract due to low temperatures.

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

Likewise, some research has shown that negative thermal expansion also occurs in single-component lattices in compact form and with a central force interaction.

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


When calculating the expansion of a physical object, it must be taken into consideration that, depending on the change in temperature, said object can increase or contract in size.

Some objects do not require a drastic change in temperature to change their size, so it is likely that the value returned by the calculations is average.

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

Linear dilation

A single variation predominates in linear dilation. In this case, the only unit that undergoes a change is the height or width of the object.

An easy way to calculate this type of dilation is by comparing the value of the magnitude before the temperature change with the value of the magnitude after the temperature change.

Volumetric dilation

In the case of volumetric expansion, the way to calculate it is by comparing the volume of the fluid before the change in temperature with the volume of the fluid after the change in temperature. The formula to calculate it is:

Thermal expansion

Surface or area dilation

In the case of surface dilation, an increase in the area of ​​a body or object is observed due to a change in its temperature at 1 ° C.

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

A f = A 0 [1 + YA (T f – T 0 )]

In this expression:

γ = coefficient of area expansion [° C -1 ]

A 0 = Initial area

A f = Final area

T 0 = Initial temperature.

T f = Final temperature

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


First exercise (linear dilation)

The rails that make up the track of a train made of steel have a length of 1500 m. What will the longitude be when the temperature goes from 24 to 45 ° C?



Lο (initial length) = 1500 m

L f  (final length) =?

Tο (initial temperature) = 24 ° C

T f  (final temperature) = 45 ° C

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

The data is substituted in the following formula:

Thermal expansion

However, you must first know the value of the temperature differential, 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 information is known, it is possible to use the previous formula:

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 high school a glass store has an area of ​​1.4 m ^ 2, if the temperature is 21 ° C. What will its final area be as the temperature increases to 35 ° C?


Af = A0 [1 + (Tf – T0)]

Af = 1.4 m [1] 204.4 x 10 -6 ]

Af = 1.4 m 2  . 1,0002044

Af = 1.40028616 m 2

Why does dilation happen?

Everyone knows that all material is made up of various subatomic particles. By altering the temperature, either raising it or lowering it, these atoms begin a process of movement that can modify the shape of the object.

When the temperature is raised, the molecules begin to move rapidly due to the increase in kinetic energy, and thus the shape or volume of the object will increase.

In the case of negative temperatures, the opposite happens, in this case the volume of the object tends to contract due to low temperatures.


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