What is Thermal expansion?

Thermal expansion is the increase in the dimensions of a material as its temperature rises. When the temperature in a material is increased, the particles in a substance gain energy and move with much more vigor in that material, causing the material to expand. It is one of the most essential phenomena in various fields, which range from engineering to construction and other mundane applications.

Types of Thermal Expansion:

• Linear Expansion: It occurs in one dimension (length).

• Area Expansion: This occurs in two dimensions that is, surface area.

• Expansion in Volume: Occurs along three dimensions of volume.

Formulae 

Formulas of various thermal expansion formulas such as linear expansion, area expansion, and volume expansion are as follows,

Linear Expansion

Linear expansion is the change in length due to heat. Linear expansion formula is given as,

Where

• L0 = original length,

• L = stretched length,

• α = coefficient of stretch,

• ΔT = change in temperature,

• ΔL = change in length

Volume expansion 

Volume expansion is the change in volume due to temperature. The volume expansion formula is given as follows,

Where,

• V0 = original volume

• V = expanded volume

• αv = volume expansion coefficient

• ΔT = temperature difference

• ΔV = change in volume after expansion

Area Expansion

Area expansion occurs is the change in area because of the temperature difference. Area expansion formula is expressed as,

Where,

• A = original area

• ΔA = change in the area

• αA = area expansion coefficient,

• ΔT = Temperature difference,

• A0 = Expanded area.

Solved Example

Example: A rod of length 5 m is heated to 40°C. If the length extends to 7 m after some time. Calculate the expansion coefficient. Room temperature is 30°C.

Solution:

Given,

1. Initial length Lo = 5 m,

2. Expanded length L = 7 m

3. Change in length ΔL = 7 – 5 = 2 m

4. Temperature difference ΔT = 40°C – 30°C = 10°C

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

Thus, the expression for linear expansion is,

Length expansion coefficient is given as,

 

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