Hello students we know that according to Hooke’s law stress is directly proportional to strain (within elastic limit). This indicates that the ratio of stress and strain is constant, which is termed as modulus of elasticity. The modulus of elasticity in which study of change in volume is takes place is known as bulk modulus (K)
Let’s define the concept and derive its formula….!
The modulus of elasticity related to a change in the volume is bulk modulus (k).
Consider the spherical object of volume ‘V’ subjected to pressure ‘dP’ undergoes change in volume as shown below.
Let ‘dV’ the change in the volume of spherical object, then
∴ volume stress = force/area
∴volume stress = change in pressure = dP
Now the volume strain in the spherical object is given as,
∴ volume strain= (change in volume )/(original volume)
∴ volume strain= (dV )/V
Bulk modulus is defined as the ratio of the volume stress to the volume strain.
∴Bulk Modulus = (Volume Stress)/(Volume Strain)
This is the formula for bulk modulus of material.
Some important points to note……!
- Bulk modulus is related to change in volume hence it is applicable for solids, liquids and gases.
- It depends on temperature and a material.
Let’s go in more detail with some numerical….!
Ex:1) The cube of copper subjected to the pressure of 1010 Pa, changes its volume by 2%. Find the Bulk modulus of copper.
Here, dP=1010 Pa, dV = 2% V