Thermal Expansion: Formula, examples and applications

Thermal expansion definition

Most of the substances solids, liquid and gases expand on heating and contract on cooling. Their thermal expansions and contractions are usually small and are not noticeable. However, these expansions and contractions are important in our daily life.

The kinetic energy of the molecules of an object depends on its temperature. The molecules of a solid vibrate with larger amplitude at high temperature than at low temperature. Thus, on heating, the amplitude of vibration of the atoms or molecules of an object increases. They push one another farther away as the amplitude of vibrations increases. Thermal expansion results an increase in length, breadth and thickness of a substance.

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What is the difference between linear thermal expansion and volume thermal expansion?

Linear Thermal Expansion In Solids

It has been observed that solids expand on heating and their expansion is nearly uniform over a wide range of temperature. Consider a metal rod of length L° at certain temperature T°. Let its length on heating to a temperature becomes L. Thus

Increases in length of the rod = ΔL = L – L0

Increase in temperature = ΔT = T – T°

It is found that change in length ΔL of the solid is directly proportional to its original length length L°, and the change in temperature Δ T. That is


ΔL =αL0ΔT …….(1)

L – L0=αL0ΔT

or L =L0(1+αΔT) …..(2)

Where α is called the coefficient of linear thermal expansion of the substance.From equation (1) we get

α = ΔL/L°ΔT

Coefficient of linear expansion

 The coefficient of linear expansion α of a substance is the fraction increase in the length per kelvin rise in temperature.

Coefficient of linear expansion formula

Below given table of linear thermal expansion of some materials:

 table of linear thermal expansion

Volume Thermal Expansion

The volume of a solid also changes with the change in temperature and is called volume thermal expansion or cubical thermal expansion. Consider a solid of initial volume V° On heating, the solid to a temperature T, let its volume becomes V, then

Change in the volume of a solid ΔV = V – V°

 change in temperature  ΔT  = T – T°

Like linear expansion, the change in volume ΔV is found to be proportional to its original volume V° and change in temperature ΔT. Thus

                                             ΔV ∝   V° ΔT

                                           ΔV=βV° ΔT ……(3)

                                         V – V°=βV° ΔT

                                          V = V°(1 + βΔT)

Where β is the temperature coefficient of volume expansion.From equation (3) we get

β = ΔV/V° Δ

Coefficient of  volume expansion

 The temperature coefficient of volume expansion β is the fractional change in its volume per kelvin change in temperature.

Coefficient of  volume expansion formula

Coefficient of volume expansion formula

The coefficients of linear expansion and volume expansion are related by the equation:

β = 3 α


Values of β for different substances are given in table:coefficient of volume expansion

Consequences of Thermal Expansion

Why gaps are left in railway tracks? The expansion of solids may damage the bridges, railway tracks and roads as they are constantly subjected to temperature changes. railway trackSo provision is made during contraction for expansion and contraction with temperature. Foe example, railway tracks buckled on a hot summer day due to expansion if gaps are not left between sections.

Bridges made of steel girders also expand during the day and contract during night. They will bend if their ends are fixed. To allow thermal girder rests on rollers in the gap left for expansion.thermal expansion in bridges

Overhead transmission lines are also given a certain amount of sag so that they can contract in winter without snapping.

Applications of Thermal Expansion in everyday life

Thermal expansion is used in our daily life.


In thermometers, thermal expansion is used in  temperature measurements.

Removing tight lids

To open the cap of a bottle that is tight enough, immerse in it hot water for a minute or so. Metal cap expands and becomes loose. It would now be easy to turn it to open.


To join steel plates tightly together, red hot rivets are forced through holes in the plates. The end of hot rivets is then hammered. On cooling, the rivets contract and bring the plates tightly gripped.

Fixing metal tires on wooden wheels

Iron rims are fixed on wooden wheels of carts. Iron rims are heated. Thermal expansion allows them to slip over the wooden wheel. Water is poured on it to cool. The rim contracts and becomes tight over the wheel.

Bimetallic Strip

bimetalic strips

A bimetal strip consists of two thin strips of different metals such as brass and iron joined together. On heating the strip, brass expands more than iron. This unequal expansion causes bending of the strip.

bimetal strips are used for various purposes. Bimetal thermometers are used to the measure temperature especially in furnaces and ovens. Bimetal strips are used in thermostats. Bimetal thermostat is used to control the temperature of heater coil in an electric iron.


Thermostat is a heat regulating device which work on the principle of thermal expansion.

Stay tuned with us to see applications of expansion:

Thermal expansion examples

  • Cracks in the road when the road expand on heating.
  • Sags in electrical power lines.
  • Windows of metal framed need rubber spacers to avoid thermal expansion.
  • Expansion joints (like joint of two railway tracks).
  • Length of metal bar getting longer on heating.
  • Tyre bursts in hot days when filled full of air due to thermal expansion.

Thermal Expansion of Liquids

The molecules of liquids are free to move in all directions within the liquid.On heating a liquid, the average amplitude of vibration of its molecules increases. The molecules push each other and need more space to occupy. The accounts for the expansion of the liquid when heated. The thermal expansion in liquids is greater than solids due to the weak forces between their molecules. Therefore, the coefficient of volume expansion of liquids is greater than solids.

Liquids have no definite shape of their own. A liquid always attains shape of their container in which it is poured.Therefore,when a liquid is heated, both liquid and the container undergo a change in their volume. Thus, there are two types of thermal volume expansion for liquid.

  • Apparent volume expansion
  • Real volume expansion

Anomalous Expansion of water

Water on cooling below 4 C° begins to expand until it reaches 0°C.On further cooling its volume increases suddenly as it changes into ice at 0°C.When ice is cooled below 0°C,it contracts i.e,its volume decreases like solids.This unusual expansion of water is called the anomalous expansion of water.


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