Coefficient of Linear Expansion

What Is Coefficient Of Linear Expansion?

To put simply, linear expansion is the phenomena of increase in the length of a specimen or material because of the rising temperature of this same material. Consequently, the coefficient of linear expansion is expressed as the per degree Celsius, or change in the length of a 1 unit long material when there is a 10 C rise in temperature. 

Coefficient of Linear Expansion Formula

As per the definition, the formula is expressed as 

αL1 = ∆L / ∆T, or 

αL1 = dL / dT,

Where, 

  • α define coefficient of linear expansion. 

  • L1 is the initial length of the material.

  • dL indicates a unit change in length. 

  • dT indicates a unit change in temperature. 

SI unit & Dimension 

The SI unit of coefficient of linear expansion can be expressed as °C-1 or °K-1. Here, C indicates Celsius and K indicate Kelvin. 

The dimension of coefficient of linear expansion will be [M^0L^0T^0K^-1]. 

Numerical for You 

Q1. A metal rod is of length 64.576 cm at a temperature 90°C whereas the same metal rod has a length of 64.522 cm at a temperature 12°C. Calculate the coefficient of linear expansion. 

Ans: Consider L2 as 64.576 cm and L1 as 64.5222; then the value of dL will be 0.054. Consider T2 as 90°C and T1 as 12°C then the value of dT will be 78. Subsequently, from the formula, α will be 1.073 x 10-5/ °C. 

The Functioning of Linear Expansion 

Every material is packed with numerous atoms and the extent to which it can expand entirely depends upon the cohesive force between these particles. In simpler words, if the cohesive force is high, then the expansion in length of the material will be low even when the temperature is increased. 

From the above, it can be concluded that the coefficient of linear expansion is an inherent property of a material, and it will vary from one element to another. For instance, soft metals expand quickly as the cohesive force between their atoms is low. 

Coefficient of Linear Expansion value for a few Compounds

Since this is the intrinsic property of a compound, each one has a different value than others, based on their properties. To define coefficient of linear expansion of solid, these have a high coefficient because of the high cohesive force between the atoms in solid. Hard solids have a higher coefficient in the range of 10-7/K, whereas organic liquids can be in the range of 10-3/K

Read on to familiarise yourself with various accessible materials and their coefficient of linear expansion. 

SI. No. 

Metals 

αL at 20°C (10-6/K)

1

Aluminium 

23.1

2

Brass

19

3

Carbon Steel 

10.8

4

Diamond

1

5

Copper 

17

6

Gold

14

7

Ice 

51

8

Iron 

11.8

9

Mercury

61

10

Steel 

11.0 ~ 13.0 

11

Water 

69

12

Silicon

2.56


Application 

This concept is popularly used in various industrial applications as well as day to day operations, like opening the lid of a tight bottle by dipping it in hot water. Here are a few other applications related to this same concept. 

  • The idea is used in thermometers for measuring temperature. 

  • Riveting. 

  • Thermostats. 

  • Development of firm buildings. 

  • In the creation of metal alloys. 

These are a few concepts which will help you understand the idea of coefficient of linear expansion equation better.

To get a better understanding, Vedantu app can help you get a comprehensive picture of this concept while helping you solve various tricky questions. Download our app to get access to carefully curated study material by proficient teachers. 

FAQ (Frequently Asked Questions)

1. What is the coefficient of linear expansion of aluminium?

The value of αL for aluminium at 20°C (10-6/K) is 23.1. This leads to a fractional change in length of aluminium at a temperature 20°C when there is a per unit rise in temperature.

2. What is the coefficient of linear expansion of steel?

The value of αL for steel at 20°C (10-6/K) is between 11.0 and 13.0. This leads to a minor change in length of Steel at a temperature 20°C when there is a unit increase in temperature.

3. Which metal has the highest coefficient of expansion?

Ti-Nb alloys are considered to have the highest coefficient of expansion. In these alloys, the value of αL will be around + 163.9×10-6 to −95.1×10-6 °C-1.