# Thermal Expansion Formula

## What is the Thermal Expansion Formula?

The tendency of an object to change its dimension in length, or volume as a result of heat is known as thermal expansion. The kinetic energy of a material increases as it is heated. There are three different types of thermal expansion formula are linear expansion, area expansion, and volume expansion. Here, we will discuss the thermal expansion equation along with its types. We will learn coefficient formulas such as the coefficient of volume expansion formula and solve problems related to it.

### Linear Expansion Formula

Expansion means, change or increase in length. A change in length over one dimension (length) over a volume is known as linear expansion. In this case, the expansion is caused by a change in temperature. As a consequence, a change in temperature is expected to cause a change in the rate of expansion. This description describes how long a substance can maintain its original shape and size when subjected to heat radiation. The change in length caused by heat is known as linear expansion. Linear expansion formula is given as,

$\frac{\delta L}{L_{0}}$ = α$_{L}$$\delta$T

Where,

L0 = original length,

L = expanded length,

α = length expansion coefficient,

ΔT = temperature difference,

ΔL = change in length

### Coefficient of Linear Expansion Formula

The Coefficient of Linear Expansion refers to the rate of change of unit length per unit degree change in temperature

Mathematically, the Coefficient of linear expansion formula can be written as:

α$_{L}$ = $\frac{dL}{dT}$

Where Tis the coefficient of linear expansion.

dL is the unit change in length

dT is the unit change in temperature

The above formula is also known as the formula of coefficient of linear expansion.

The S.I unit is: ⁰ C⁻¹ or K⁻¹

### Applications of Coefficient of Linear Expansion

Scientific and technical advancements have tremendous benefits. To keep up with the rapid growth of industrialization and construction, the material palette's implementation must be certain. From the construction of a house to the launch of a satellite, the material used serves as a backbone.

A wide range of materials is readily available all around us. They all have different thermal properties. In order to use materials properly, it's important to compare their expanding capacities as temperature rises. Materials with a higher linear expansion coefficient are more stable and can be used to build solid structures in general. This property can be customized to suit specific needs by mixing the materials. Metal alloys are becoming more popular as a result of this.

### Volume Expansion Formula

The change in volume caused by temperature is known as volume expansion. The volume expansion formula is given as

$\frac{\delta V}{V_{0}}$ = α$_{V}$$\delta$T

V$_{0}$ = original volume,

V = expanded volume,

α$_{V}$ = volume expansion coefficient,

ΔT = temperature difference,

ΔV = change in volume after expansion

### Volumetric Expansion Coefficient

Since most of the objects we use in real life are three-dimensional and thus undergo three-dimensional expansion (volumetric expansion), it is important that we consider the volumetric thermal expansion of substances.

### Thermal Expansion of Solids Examples

Thermal expansion has many applications in everyday life. The following are a few of them:

• Metal hot water heating pipes with long straight lengths should not be used.

• Rubber spacers are needed for metal-framed windows.

• To avoid sub-kinking, large structures and mega constructions such as railways and bridges need expansion joints.

• Thermometers are another example of a thermal expansion device.

### Solved Example:

1. A 5 m long rod that has been heated to 40°C. After some time, the length increases to 7 m. Find the coefficient of expansion. The room temperature is 30°C.

Ans: Given:

Initial length L0 = 5 m,

Expanded length L = 7 m

Change in length is denoted by Δ L = 7 – 5 = 2 m

Temperature difference Δ T = 40°C – 30°C  = 10°C

Absolute temperature T = 10°C +273=283 K

The linear expansion formula is given by,

$\frac{\delta L}{L_{0}}$ = α$_{L}$$\delta$T

∴  Length expansion coefficient is given by,

α$_{L}$ = $\frac{\delta L}{L_{0} \times \delta T}$

α$_{L}$ = $\frac{2}{5 \times 283}$

α$_{L}$ = 14 x 10$^{-4}$K$^{-1}$

### Conclusion

Following are points we can conclude from above,

• Due to a change in temperature, thermal expansion causes a body's size (length, area, or volume) to increase or decrease.

• Gases have a massive thermal expansion, whereas liquids and solids have a smaller but still significant thermal expansion.

• ΔL = αLΔT is the formula for linear thermal expansion, where ΔL is the change in length L,  ΔT is the change in temperature, and is the linear expansion coefficient, which varies slightly with temperature. ΔV = βVΔT, where β is the coefficient of volume expansion and β ≈ 3α is the change in volume due to thermal expansion. When the thermal expansion is restricted, thermal stress is produced.

• The coefficient of thermal expansion formula explains how an object's size increases as the temperature changes.

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1. What is the Coefficient of Linear Thermal Expansion?

Ans: The coefficient of linear thermal expansion is defined as a material's relative expansion divided by its temperature change.

2. What are the Basic Properties of Thermal Expansion?

Ans: Thermal expansion is directly proportional to temperature change. A bimetallic strip can bend further as the temperature changes. Second, it is material dependent. For example, the expansion of alcohol in a thermometer is much greater than the expansion of the glass in which it is contained.

3. Define Volumetric Thermal Expansion Coefficient.

Ans: The volumetric coefficient is the most fundamental thermal expansion coefficient. As a substance's temperature increases, it expands or contracts in all directions, as seen in this diagram. Isotropic drugs are those that extend in all directions.

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