How is bulk modulus related to the compressibility of a material?

Bulk modulus is directly proportional to the compressibility of a material.

Bulk modulus is a measure of a material's resistance to compression. It is defined as the ratio of the applied pressure to the resulting fractional decrease in volume. The higher the bulk modulus, the more difficult it is to compress the material. Conversely, a lower bulk modulus indicates that the material is more compressible.

The relationship between bulk modulus and compressibility can be expressed mathematically as K = -V(dP/dV), where K is the bulk modulus, V is the volume of the material, and dP/dV is the rate of change of pressure with respect to volume. This equation shows that the bulk modulus is inversely proportional to the compressibility of the material.

In practical terms, materials with a high bulk modulus, such as diamond, are very difficult to compress, while materials with a low bulk modulus, such as rubber, are easily compressed. This relationship is important in many applications, such as in the design of hydraulic systems, where materials with a high bulk modulus are preferred to prevent excessive deformation under pressure.