# Bulk Modulus: Definition, Formula, Examples, Compressibility, Application

Consider you have two balloons filled with two different gases. Now if I ask you to compress these balloons and tell me which gas is easier to compress than others. So to know which gas is easier to compress you will normal stress on it and see which balloon is getting shrinked. So the gas which gets compressed by applying a small amount of force will be considered as more compressible than the gas which requires a huge amount of force. Now what if I tell you that there is a quantity in physics known as Bulk Modulus which gives the information about the fluid regarding its compressibility. So in this article let’s learn about Bulk Modulus.

• Bulk modulus
• Bulk Modulus of Different Materials
• Relation between density, pressure and bulk modulus
• Compressibility
• Practice problems
• FAQs

## Bulk Modulus

The bulk modulus is the proportion of volumetric stress related to the volumetric strain of specified material, while the material deformation is within the elastic limit. To put in more simple words, the bulk modulus is nothing but a numerical constant that is used to measure and describe the elastic properties of a fluid when pressure is applied on all the surfaces. It is defined as the ratio of the normal stress to the volumetric strain. It is important to remember

that it has dominance only on the fluids (i.e., on liquids and gases).

Normal stress or longitudinal stress is given by the following equation,

Note: negative sign means volume is reduced.

Hence the bulk modulus is mathematically written as,

Bulk modulus has the same unit and dimension as pressure or stress.

Comparison of bulk modulus for solids, liquids and gases is as follow:

## Relation between Density, Pressure and Bulk Modulus

When a pressure is applied on a substance having density and bulk modulus , then its volume changes from to . Hence,

………..(1)

………..(2)

From above equations,

Therefore,

## Compressibility

The reciprocal of bulk modulus of elasticity is called compressibility. It is detonated by the letter K.

So

The SI unit of compressibility is or .

Dimension of compressibility K is

Comparison of compressibility for solids, liquids and gases is as follow:

Note: It is difficult to compress the gases that have a higher value of bulk modulus. In other words, higher the value of compressibility, easier it is to compress the gases as .

## Practice Problems

Q. Calculate the density of water near the bottom of ocean where the pressure is about and density of water is approximately. Take bulk modulus of water as .

A. The density of water at the ocean’s surface where the pressure is is about Thus, of water at the surface has a mass of . Let us calculate the change in volume of this water when it is ar a pressure of .

The pressure change , which is equivalent to . Thus the volume change is

The density of water is then,

Q. A hydraulic press contains of oil. Find the decrease in volume of the oil when it is subjected to a pressure increase . The bulk modulus of the oil is .

A.

Q. Compressibility of water is . Find the decrease in volume of of water when subjected to a pressure of .

A. The compressibility K is the reciprocal of the bulk modulus.

The decrease in volume is thus .

Q. Bulk modulus of rubber is . To what depth should a rubber ball be taken in a lake so that its volume is decreased by ?

A.

Let h be the required depth and the density of water be then

## FAQs

Q. What is the effect of pressure on the bulk modulus?

A. Bulk modulus is independent of pressure as it is material property.

Q. What is the product of bulk modulus and compressibility?

A.

Q. Which state of matter has the highest bulk modulus?

A. Solid has the highest bulk modulus.

Q. What is the significance of negative sign in the formula for bulk modulus?

A. The negative sign is used in the formula of bulk modulus to compensate for the negative value of change in volume in case of compression of volume. Therefore the bulk modulus will never be negative.