Question: Define bulk modulus of elasticity how is compressibility related with bulk modulus of elasticity?
In this blog post, we will learn about the concept of bulk modulus of elasticity, which is one of the measures of the mechanical properties of solids and fluids. We will also see how compressibility is related to bulk modulus of elasticity.
What is bulk modulus of elasticity?
Bulk modulus of elasticity is defined as the ratio of the applied pressure to the relative decrease in volume of a material when it is under pressure on all surfaces. It is a numerical constant that describes the elastic properties of a solid or fluid, i.e., how much it will compress under a given amount of external pressure. The bulk modulus of elasticity is denoted by the symbol K, and it has the dimension of force per unit area. It is expressed in the units of pascal (Pa) or newton per square meter (N/m^2) in the SI system.
Mathematically, we can write the formula for bulk modulus of elasticity as:
K = ΔP / (ΔV/V)
Where:
K: Bulk modulus
ΔP: Change of the pressure or force applied per unit area on the material
ΔV: Change of the volume of the material due to the compression
V: Initial volume of the material
How is compressibility related to bulk modulus of elasticity?
Compressibility is a measure of how much a material can be reduced in volume by applying pressure. It is the inverse of bulk modulus of elasticity, i.e.,
β = 1/K
Where:
β: Compressibility
K: Bulk modulus
The higher the value of K for a material, the lower its compressibility and vice versa. For example, steel has a high value of K (about 1.6×10^11 N/m^2) and a low value of β (about 6.25×10^-12 m^2/N), which means that steel is very incompressible and resistant to volume change under pressure. On the other hand, gases have very low values of K and very high values of β, which means that gases are very compressible and easily change their volume under pressure.
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