In physics, Thermal expansion can be defined as the change in the length, width, height or volume of any material on changing the temperature. Thermal expansion is very evident in solids as atoms are densely packed. Thermal expansion of solids have loads of applications in day to day life.

## Thermal Expansion in Metals

It is a well-known phenomenon now that substances expand on heating and contract on cooling. If you heat a body, it alters its dimensions. Depending on the shape of the body.

- The expansion can occur in length in which case it is called Linear Expansion.
- If we take a square tile and heat it, the expansion will be on two fronts, length and breadth, here it is called Area Expansion.
- If we take a cube and heat it, all its sides expand and now the body experiences an increase in the overall volume due to this and it is called Volume Expansion.

## Thermal Expansion Formula

Thermal expansion can result in linear expansion or area expansion or volumetric expansion. The corresponding formula is given below along with relevant terms. Thus, the formula used to represent the thermal expansion in a body is

**Linear Expamsion:**

where,

- l is the initial length of the solid
- Δl is the change in length.
- α
_{l}length expansion coefficient - ΔT is the temperature difference

**Area Expamsion:**

where,

- A is the initial area of the solid
- ΔA is the change in area.
- α
_{A}Area expansion coefficient - ΔT is the temperature difference

**Volumetric Expamsion:**

where,

- V is the initial volume of the solid
- ΔV is the change in volume.
- α
_{V}volume expansion coefficient - ΔT is the temperature difference

Here, the alpha_{l} represents the coefficient of linear expansion and it is a characteristic of the substance the body is made of. For example, for the same temperature rise, copper expands almost five times more than glass. Generally, metals expand more and have higher values of alpha compared to gases and liquids.

### Volumetric Expansion Coefficient

It is important that we consider the volumetric thermal expansion of substances since most of the things we use in real life are three dimensional and thereby undergo three-dimensional expansion ie volumetric expansion.

## Coefficient Of Thermal Expansion Table

Value of coefficient of thermal expansion of different solids are very important to choose the right material. The table is given below lists the name of the material along with the corresponding coefficient of thermal expansion values

Material | Linear Expansion Coefficient α_{l} at 20^{°}C 10^{-6}K^{-1} |
Volumetric Expansion Coefficient α_{v} at 20^{°}C 10^{-6}K^{-1} |
---|---|---|

Quarts | 0.59 | 1.77 |

Diamond | 1 | 3 |

Stainless steel | 10.1~17.3 | 30.3~51.9 |

Steel | 11~13 | 33.0~39.0 |

Iron | 11.8 | 35.4 |

Concrete | 12 | 36 |

## Thermal Expansion Of Solids Examples

One can observe a plethora of applications of Thermal expansion in day to day life. Some of them are:

- Metal hot water heating pipes should not be used in long straight lengths
- Metal framed windows need rubber spacers
- Large structures and mega constructions such as railways, bridges need expansion joints in the structures to avoid sub kink
- Thermometers are another example of an application of thermal expansion

In the case of the thermometer, the liquid is constrained to flow in only one direction that is along the tube due to changes in volume brought about by changes in temperature. The working principle of mercury thermometer is explained below.

### Mercury Thermometer

Thermal expansion is the basic principle that a thermometer works on. The mercury in the reservoir at the bottom of the thermometer is immersed in a hot or cold object. On doing so, the mercury in the thermometer contracts and expands changing the level indicated on the thermometer.

The thermometers are always calibrated and after a few minutes, the level of mercury inside becomes stable and unchanging. This new level with the calibrated thermometer tells us the temperature of the object we are measuring. The same principle of thermal expansion applies to gases as well. The constant volume gas thermometer is an example of the application of thermal expansion in gases.

**Physics Related Links:**

Thermal stress | Relation Between Density And Temperature |

Properties of Water : Anomalous Expansion of Water | Important Questions Class 11 : Chapter 10 – Thermal Properties of Matter |

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