# Bulk Modulus of Elasticity

## Bulk Modulus of Elasticity

Bulk modulus of elasticity is one of the measures of mechanical properties of solids. Other elastic modules include Young’s modulus and Shear modulus. In any case, the bulk elastic properties of a material is used to determine how much it will compress under a given amount of external pressure.

What is a Bulk Modulus of Elasticity?

The ratio of normal stress to volume strain within elastic limit is called Bulk Modulus of Elasticity of a given material. It is denoted by K.

Suppose a force F is applied normal to a surface of a body having cross sectional area equal to A. If applied force brings about a change ΔV in the volume of the body and V is the original volume of the body then,

$$Normal\,Stress\,=\,\frac{F}{A}$$, $$Volume\,Strain\,=\,\frac{\Delta V}{V}$$.

Now, Bulk Modulus of Elasticity would be,

$$Bulk\,Modulus(K)\,=\,\frac{Normal\,Stress}{Volume\,Strain}=\frac{FV}{A\Delta V}=\frac{\Delta P}{\left( \frac{\Delta V}{V} \right)}$$.

∴ $$Bulk\,Modulus(K)=\frac{\Delta P}{\left( \frac{\Delta V}{V} \right)}$$.

Where,

ΔV = Change of the Volume of the material due to the compression,

ΔP = Change of the pressure/Force applied per unite area on the material,

V = Initial volume of the material in the units of N/ m².

For gases and liquids the normal stress is caused by change in pressure.

i.e., Normal stress = Change in pressure (ΔP).

Thus, $$Bulk\,Modulus(K)\,=\,-\frac{V\Delta P}{\Delta V}$$.

Here, negative sign indicates that the volume decreases, if pressure increases and vice versa.