Thermal expansion: what it is, formula and examples

Thermal expansion: what it is, formula and examples

Thermal expansion is the physical phenomenon in which a material experiences a change in its dimensions due to variations in temperature.

When the temperature of an object is increased, the particles that compose it tend to move with greater energy and amplitude, which causes an increase in intermolecular space and, consequently, in its macroscopic dimensions.

Thermal expansion is a relevant phenomenon in many practical applications and can have significant effects on structures, mechanical systems and thermal devices. Engineers and designers must consider these effects when designing components and systems that will be subject to temperature changes.

There are three main types of thermal expansion: linear expansion, superficial expansion, and volumetric expansion.

Linear expansion

Linear expansion is a type of thermal expansion that occurs in one-dimensional objects, such as bars, rods, or cables, when subjected to changes in temperature. 

When an object is heated, the particles that compose it acquire greater kinetic energy and move away from each other, causing an increase in the length of the object. 

The formula to calculate the linear expansion of an object is as follows:

ΔL = α * L0 * ΔT


  • ΔL is the variation in length.

  • L0 is the initial length.

  • α is the coefficient of linear expansion of the material.

  • ΔT corresponds to the temperature change.

Superficial expansion

Superficial expansion is another type of thermal expansion that occurs in two-dimensional objects, such as sheets, plates, or flat surfaces, when subjected to changes in temperature.

The variation of the surface area (ΔA) is related to the initial area (A0), the coefficient of surface expansion (β) of the material and the change in temperature (ΔT) by the following equation: ΔA = β * A0 * ΔT

The coefficient of superficial expansion (β) is twice the coefficient of linear expansion (α): β = 2 * α

Volumetric expansion

Volumetric expansion refers to the change in the volume of a three-dimensional object due to variations in temperature.

The dimension affected is the volume. The volume variation (ΔV) is related to the initial volume (V0), the volumetric expansion coefficient (γ) of the material and the temperature change (ΔT) by the following equation: ΔV = γ * V0 * ΔT.

The coefficient of volumetric expansion (γ) indicates how much the volume of the object will expand or contract per unit temperature change and is three times the coefficient of linear expansion (α): γ = 3 * α

Coefficient of expansion

Each material has a specific coefficient of expansion that determines how much it will expand or contract per unit temperature change. Materials with higher coefficients of expansion tend to experience greater thermal expansion with increasing temperature.

The coefficients of superficial and volumetric expansion are twice and three times the coefficient of linear expansion, respectively.

Coefficients of linear expansion are generally expressed in units of 10-6 per degree Celsius (μm/°C) or 10-6 per degree Kelvin (μm/K). 

What does the thermal expansion of a material depend on?

The difference in thermal expansion between materials depends on several intrinsic characteristics of each substance.

First, the atomic structure and the type of bond in the material play a fundamental role: materials with strong bonds, such as ionic or covalent crystals, tend to have lower thermal expansion than those with weaker bonds, such as amorphous.

In addition, the atomic mass, density, and distribution of atoms also play a role, since denser materials with more massive atoms may experience less expansion compared to less dense materials.

Thermal expansion in gases

In the case of gases, the volume variation is governed by other formulas. By their nature, gases tend to occupy the entire available volume, maintaining a balanced relationship between pressure, temperature and volume.

When a gas undergoes a change in temperature, the volume varies depending on how the pressure varies according to the universal gas law.

The law of Charles and Gay-Lussac states that, at constant pressure, the volume of an ideal gas is directly proportional to its absolute temperature (measured in Kelvin). The equation that represents this relationship is:

V2 = V1 * (T2 / T1 )

Where V1 and V2 are the initial and final volumes of the gas, and T1 and T2 are the initial and final absolute temperatures, respectively.

Examples of thermal expansion in everyday life 

Thermal expansion is a common phenomenon in everyday life and can be observed in numerous objects and situations. Here are some examples:

  1. Expansion of roads and bridges: Bridges and roads are made of materials such as concrete and steel, which expand when heated and contract when cooled. For this reason, they are designed with expansion joints to prevent cracks and breaks.

  2. Train Rail Expansion: Train rails, usually made of steel, also undergo thermal expansion. As rails heat up in the sun, they can get longer, and this can lead to the need for expansion joints to prevent track warping and distortion issues.

  3. Expansion in Liquids: When a liquid is heated, its molecules gain kinetic energy and move faster, causing the volume of the liquid to increase. A common example is the thermometer, where the expansion of a liquid, such as mercury, is used to measure temperature.

  4. Expansion in Power Lines: Power cables, especially those that run long distances, can experience thermal expansion due to changes in temperature. Power lines can expand or contract, varying the shape of the catenary and the tension force that holds them at their ends.

  5. Expansion in cookware: When heating or cooling pans, saucepans, and other cookware, the materials they are made from expand or contract, which can affect their shape and fit.

Data de publicació: July 28, 2023
Última revisió: July 28, 2023