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Coefficient of Linear Expansion

Thermal expansion is defined as the property of a substance through which it changes in shape, size, area, volume etc., with a temperature change. This does not include phase transition.

When a substance is heated, its molecules acquire more kinetic energy. Now, the temperature is a monotonic function of kinetic energy. The increased energy causes the molecules to move with greater vigour. This increases the average distance between the molecules in a substance. This, in turn, is responsible for the change in size that the material experiences.

Materials do exist that contract with an increase in temperature. But such substances are very rare and are only found within certain temperature ranges.

The coefficient of linear thermal expansion of a material is defined as the ratio of strain to the change in temperature. Strain, here, is defined as the change in length of the material divided by the original length. Thus, the coefficient of thermal expansion generally changes with temperature.

When the temperature of a substance is increased, the intermolecular forces of that substance is also weakened.

Coefficient of Thermal Expansion

The coefficient of thermal expansion tells us how materials change their shape and size with the temperature change. Alternatively, it can also be said to be the ratio of change in size to the per degree change in temperature. For the calculation of the coefficient to be simplified, the pressure is taken to be constant.

In practice, this means that the materials with a low thermal expansion coefficient tend to change in their size very little with the temperature change.

Coefficients of thermal expansions are of many varieties. The coefficient of volumetric expansion is the coefficient that helps us in determining the change in the volume of a material with the change in the corresponding temperature. The volumetric coefficient is taken to be the most basic coefficient, and it is most relevant for fluids. This is because fluids are not of fixed dimensions, and the volume of a liquid is the only metric that can be determined accurately. The coefficient of area expansion is the coefficient that is concerned with the change in the area of a substance with the corresponding temperature change.

We will here describe the Linear thermal expansion coefficient of materials. The linear thermal expansion coefficient is most relevant for objects where only one dimension, say length, is of the most interest as compared to the other two dimensions. This is usually the case with solids, where we are only required to find the change in length over a certain period in changing temperatures. Some examples include rail tracks and the suspension bridge. In such structures, the length of the materials used is very important for the feasibility of construction and the safety of the users.

The formula for the linear thermal expansion is written below:

αL = dL/dT

αL is the coefficient of linear thermal expansion. The subscript ‘L’ signifies the dimension for which the coefficient is relevant
dL is the change in length
dT is the change in temperature

The substances that contract or expand at the same rate in every direction are called isotropic substances. For such substances, the volumetric expansion coefficient and the area expansion coefficient are three times and two times the linear expansion coefficient, respectively.


The coefficient of thermal expansion plays a very important role in our everyday life. Therefore, it is a very important consideration when building and designing large structures. In fact, it is one of the most basic precautions that civil engineers take before constructing any large structure is begun.

The expansion of materials is also taken care of when metal links or tapes are used for measuring large distances in land surveys. These links and tapes increase in size when they are exposed to sunlight. The sunlight causes the temperature of the links or tapes to rise and, as a result, the dimensions of the tapes or the links can change. This can cause an error in the measurement of distances.

When moulds are designed for casting very hot materials like molten metal or glass, the expansion due to change in temperature has to be considered separately, as the mould holds materials that acquire very high temperatures. If the expansion due to heat is not taken care of, the cast may come out to be faulty.

It is also applied in fitting parts over each other. For example, a bushing can be fitted over a shaft by making its diameter slightly smaller than the shaft. Then it is heated until it easily fits over the shaft. It is then allowed to cool. This results in a very firm grip of the bushing on the shaft.


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