Thermal Expansion Formula

What is Thermal Expansion

Thermal expansion is the phenomenon observed in solids, liquids, and gases. In this process, an object or body expands on the application of heat (temperature). Thermal expansion defines the tendency of an object to change its dimension either in length, density, area, or volume due to heat. When the substance is heated it increases its kinetic energy. Thermal expansion is of three types:

• Linear expansion
• Area expansion
• Volume expansion

The relative expansion of the material divided by the change in temperature is known as the coefficient of linear thermal expansion. The coefficient of linear thermal expansion generally varies with temperature.

Read more: Thermal expansion of solids

Linear Expansion

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

\(\begin{array}{l}\frac{\Delta L}{L_{o}}=\alpha _{L}\Delta T\end{array} \)

Where,

L0 = original length,

L = expanded length,

α = length expansion coefficient,

ΔT = temperature difference,

ΔL = change in length

Volume Expansion

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

\(\begin{array}{l}\frac{\Delta V}{V_{o}}=\alpha _{V}\Delta T\end{array} \)

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 due to temperature change. Area expansion formula is given as,

\(\begin{array}{l}\frac{\Delta A}{A_{o}}=\alpha _{A}\Delta T\end{array} \)

Where,

A = original area,

ΔA = change in the area,

αA = area expansion coefficient,

ΔT = temperature difference,

A0 = expanded area.

Solved Examples

Example 1

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

Solution:

Given:

Initial length Lo = 5 m,

Expanded length L = 7 m

Change in length 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,

\(\begin{array}{l}\frac{\Delta L}{L_{o}}=\alpha _{L}\Delta T\end{array} \)

∴  Length expansion coefficient is given by,

\(\begin{array}{l}\alpha _{L}=\frac{\Delta L}{L_{o}\times \Delta T}\end{array} \)

    = 2 / 5 x 283

   

\(\begin{array}{l}\alpha _{L}=14\times 10^{-4}K^{-1}\end{array} \)

See the video below, to have a clear idea about thermal expansion.

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Frequently Asked Questions – FAQs

Q1

What is thermal expansion?

Thermal expansion is the process in which an object or body expands on the application of heat.

Q2

Thermal expansion effects which properties of matter?

Thermal expansion effects the shape, volume, area, and density of the body.

Q3

What is the coefficient of linear thermal expansion?

The relative expansion of the material divided by the change in temperature is known as the coefficient of linear thermal expansion.

Q4

Do all materials have the same expansion coefficients?

No.

Q5

Do molecules start to move or vibrate when the substance is heated?

Yes.