Coefficient of Linear Expansion

What is the Coefficient of Linear Expansion?

Expansion means, change or increase in length. If the change in length is along one dimension (length) over the volume, then it is called linear expansion. Here the reason behind the expansion is the change in temperature Thus, it is implied that the change in temperature will reflect in the rate of expansion. How much material can withstand its original shape and size when it is illuminated by the heat radiation is well explained using this concept.

The Coefficient of Linear Expansion can be defined as:

“The rate of change of unit length per unit degree change in temperature”

Assuming the effect of pressure is negligible.

Coefficient of Linear Expansion Formula

The coefficient of linear expansion can be mathematically written as:

\(\alpha _{L}=\frac{dL}{dT}\)

Where,

  • \(\alpha _{L}\) is the coefficient of linear expansion.
  • \(dL\) is the unit change in length
  • \(dT\) is the unit change in temperature.

S.I. Unit

The S.I unit is: \(^{\circ}C^{-1} or K^{-1}\)

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How does it work?

The linear expansion coefficient is an intrinsic property of every material. Hence it varies from one material to another. The rate at which a material expands purely depends on the cohesive force between the atoms. Cohesive force is the force that binds two or more atoms.

In other words, the cohesive force resists the separation between the atoms. However, the greater the cohesive force, the expansion will be low for a given increase in temperature. The soft metals like, Lead has a low melting point and can be compressed easily. On heating, the lead will expand faster with a unit rise in temperature.

Applications of Coefficient of Linear Expansion

The outcome of advancement in science and technology are immense. To march with this rapid growth in industrialisation and constructions, one needs to be sure about the usage of the material palette. Starting from constructing a building till constructing a satellite, The material used act as a backbone.

The diverse variety of materials are readily available around us. Each of them has different thermal properties. Comparing the expanding ability with an increase in temperature for various material is crucial to use them in an appropriate situation. Generally, the material with a higher linear expansion coefficient is strong in nature and can be used in building firm structures. This property can be modified to match the need by mixing the materials. Thus nowadays metal alloys are getting popular.

Coefficient of Linear Expansion for various materials

This session mainly summarizes the coefficient of linear expansion for various materials. Some material shows huge variation in \(\alpha _{L}\) when it is studied against variation in temperature and pressure.

For hard solids \(\alpha _{L}\) ranges approximately around \(10^{^{-7}} K^{-1}\) and for organic liquids \( \alpha _{L}\) ranges around \(10^{^{-3}} K^{-1}\). Highest \(\alpha _{L} \)is observed for Ti-Nb alloy.

Below is the table of materials along with their \(\alpha _{L}\) values.

Metals
Coefficient of linear expansion \(\alpha _{L}\) at \(20^{\circ}C\) (\(10^{^{-6}} K^{-1}\))
Aluminium
23.1
Benzocyclobutene
42
Brass
19
Carbon steel
10.8
Concrete
12
Copper
17
Diamond
1
Ethanol
250
Gallium(III) Arsenide
5.8
Gasoline
317
Gold
14
Ice
51
Iron
11.8
Lead
29
Magnesium
26
Mercury
61
Nickel
13
Platinum
9
Stainless steel
10.1~17.3
Steel
11.0~13.0
Water
69
Silicon
2.56
Silver
18

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Practise This Question

An electric dipole consisting of two opposite charges of magnitude 2×106C  each, separated by a distance of  3 cm is placed in an electric field of 2×105N/C. The maximum torque on the dipole will be