**Expansion of Solids **

### Key Concepts

- Introduction
- Linear expansion
- Areal expansion
- 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:

- Linear expansion

- Areal expansion

- Volumetric expansion

**Linear expansion:**

Let us consider an iron rod of length L_{1} at temperature T_{1}. When the iron rod is subjected to constant heat, it expands, and its length changes from L_{1 }to L_{2} and the temperature to T_{2}.

The coefficient of linear expansion is given by:

Where,

α = Coefficient of linear expansion

L_{1} = Length of the iron rod before heating

L_{2} = Length of the rod after heating

T_{1} = Initial temperature of the rod

T_{2} = Final temperature of the rod after expansion

**Points to be remembered:**

- Linear expansion is only affecting the length.

- It has only one dimension (Length).

- The coefficient of linear expansion is only one dimensional.

**Areal expansion:**

Let us consider an iron sheet of area A_{1} at temperature T_{1}, and the iron sheet is heated constantly. After some time, the area of the iron sheet changes from A_{1} to A_{2} at temperature T_{2.}

Then the coefficient of areal expansion is given by:

Where,

β = Coefficient of areal expansion

A_{1} = Area of the iron sheet before heating

A_{2} = Area of the iron rod after heating

T_{1} = Initial temperature of the sheet

T_{2} = Final temperature of the sheet after expansion

**Points to be remembered:**

- Areal expansion is only on the area.

- It has two-dimensions (Area).

- The coefficient of areal expansion is only two dimensional.

**Volumetric expansion:**

Let us consider an iron block with the volume V_{1} at the temperature T_{1, }and the block is heated constantly. If the volume of the block is changed from V_{1} to V_{2} at the temperature T_{2,}

then the coefficient of volumetric expansion is given by:

Where,

γ = Coefficient of volumetric expansion

A_{1} = Volume of the iron block before heating

A_{2} = Volume of iron block after heating

T_{1} = Initial temperature of the block

T_{2} = Final temperature of the block after expansion

**Points to be remembered:**

- Volumetric expansion is only on the volume.

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

**Summary**

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

- Linear expansion
- Areal expansion
- 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:

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