Expansion of Solids – Types of Expansion

Expansion of Solids  

 Key Concepts

1. Introduction
2. Linear expansion
3. Areal expansion
4. Volumetric expansion

Explanation

Introduction: 

In this session, we will learn about the effect of heat, particularly on the solids.  

Solids show three types of expansions when exposed to heat, they are: 

1. Linear expansion 

2. Areal expansion 

3. Volumetric expansion 

Linear expansion: 

Let us consider an iron rod of length L₁ at temperature T₁. When the iron rod is subjected to constant heat, it expands, and its length changes from L₁ to L₂ and the temperature to T₂.  

The coefficient of linear expansion is given by: 

Where, 

α = Coefficient of linear expansion 

L₁ = Length of the iron rod before heating 

L₂ = Length of the rod after heating 

T₁ = Initial temperature of the rod 

T₂ = Final temperature of the rod after expansion 

Points to be remembered: 

1. Linear expansion is only affecting the length. 

2. It has only one dimension (Length). 

3. The coefficient of linear expansion is only one dimensional. 

Areal expansion: 

Let us consider an iron sheet of area A₁ at temperature T₁, and the iron sheet is heated constantly. After some time, the area of the iron sheet changes from A₁ to A₂ at temperature T_2. 

Then the coefficient of areal expansion is given by: 

Where, 

β = Coefficient of areal expansion 

A₁ = Area of the iron sheet before heating 

A₂ = Area of the iron rod after heating 

T₁ = Initial temperature of the sheet 

T₂ = Final temperature of the sheet after expansion 

Points to be remembered: 

1. Areal expansion is only on the area. 

2. It has two-dimensions (Area). 

3. The coefficient of areal expansion is only two dimensional. 

Volumetric expansion: 

Let us consider an iron block with the volume V₁ at the temperature T_1, and the block is heated constantly. If the volume of the block is changed from V₁ to V₂ at the temperature T_2, 

then the coefficient of volumetric expansion is given by: 

Where, 

γ = Coefficient of volumetric expansion 

A₁ = Volume of the iron block before heating 

A₂ = Volume of iron block after heating 

T₁ = Initial temperature of the block 

T₂ = Final temperature of the block after expansion 

Points to be remembered: 

1. Volumetric expansion is only on the volume. 

2. It has a three-dimensions (volume). 
3. The coefficient of areal expansion is three dimensional

Summary

Solids show three types of expansions when exposed to heat, they are:

1. Linear expansion
2. Areal expansion
3. Volumetric expansion

The coefficient of linear expansion is given by:

Then the coefficient of areal expansion is given by

Then the coefficient of volumetric expansion is given by: