Thermal Expansion Formula

Thermal Expansion Formula

Thermal expansion describes the tendency of an object to change in its area, volume and shape to a shift in temperature through a transfer of heat. Heat is a consistently decreasing function of the average molecular kinetic energy of an object. Heating up a substance increases its kinetic energy.

Since thermal expansion leads to changes in dimension either in length or volume, therefore, there are three types of thermal expansion namely – Linear expansion, Area expansion, and Volume expansion.  

  1.    Linear expansion occurs when there is a change in the length. Linear expansion formula is given as,

Where,

L0 = original length,

L = expanded length,

α = length expansion coefficient,

ΔT = temperature difference,

ΔL = change in length.

    1.     Volume expansion occurs when there is a change in volume due to temperature. Volume expansion formula is given as

Where,

V0 = original volume,

V = expanded volume,

αv = volume expansion coefficient,

ΔT = temperature difference,

ΔV = change in volume after expansion.

    1.     Area expansion occurs when there is any change in area due to temperature change. Area expansion formula is given as,

Where,

A = original area,

ΔA = change in area,

αA = area expansion coefficient,

ΔT = temperature difference,

A0 = expanded area.

Example 1

A 5m long rod is heated to 40oC. If the length of the rod expands to 7m after some time, calculate the expansion coefficient. Given room temperature is 30o 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 = 40o C – 30o  = 10o C

   = 283 K

The linear expansion formula is given by,

ΔL / Lo = αL Δ T

 Length expansion coefficient is given by,

αL = ΔL / Lo×ΔT

    = 2 / 5 x 283

   αL = 14 × 10-4 K-1.

Example 2:

A volume of a balloon changes from 4 cm to 10 cm. Determine the change in its volume.

Solution:

Given:

Original volume Vo = 4 cm,

Volume expansion V = 10 cm

The change in volume is given by

Δ V = V – Vo

  = 10 – 4

  = 6 cm.

 

 


Practise This Question

Jessica and Jenny are bright students in your class. Both of them are toppers thus they have good competition between them. Now, as your final term examination was over, Jessica was very scared of her result as she could not do so well. Next day, the results were out and it was represented in a graphical manner.
Here the horizontal axis is x axis which represents  subjects  and vertical axis is y axis which represents marks. The scale for x axis is 1cm = 1 subject and y axis 1cm = 10 marks.

The bar graph shows the scores, Jessica obtained in her end of year exams. Jenny's score in English was 15% higher than Jessica's score in English. What was Jenny's score in English?