The bulk modulus or volume modulus is a property that determines how much a material resists being squeezed or compressed. When pressure is applied to a material, its volume typically decreases, becoming smaller. The bulk modulus quantifies the change in a material’s volume when subjected to increased pressure.
In simple terms, the bulk modulus indicates how “rigid” or “compressible” a material is when pressure is applied. Materials with a high bulk modulus, like metals or diamonds, are harder to compress, while materials with a low bulk modulus, like rubber or air, are easier to compress.
Formula
When pressure is applied uniformly to a material, its volume changes. The relative change in volume can be quantified using a term called volumetric strain. It is defined as the change in volume (ΔV) divided by the original volume (V 0 ):
Bulk modulus (K) is mathematically represented as the ratio of the change in applied pressure (ΔP) to the volumetric strain:
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The negative sign in the bulk modulus formula indicates that an increase in pressure results in a decrease in volume, reflecting the inverse relationship between pressure and volume in compression. A material with a high bulk modulus will experience a small change in volume when pressure is applied, meaning it is more resistant to compression. Conversely, a material with a low bulk modulus will compress more easily under the same amount of pressure.
Unit
The bulk modulus is measured in Pascals (Pa), the SI unit for pressure.
Applications
- Engineering: Used in designing materials that need to withstand high pressures, such as submarine hulls, hydraulic systems, and pressurized tanks
- Earth Sciences : Crucial for understanding seismic waves as they travel through different layers of the Earth, which depends on the compressibility of materials.
- Fluid Mechanics : Essential for analyzing the compressibility of fluids, like air and water, especially in high-pressure situations (e.g., deep-sea exploration, aerodynamics).
- Materials Science : Key in selecting and designing materials for applications requiring low compression, such as aircraft, automobile components, and biomedical devices.
Example Problems with Solutions
Problem 1 : A metal cylinder has an initial volume of 5.0 x 10 -3 m 3 . When a pressure of 2.0 x 10 6 Pa is applied, the volume decreases by 1.0 x 10 -4 m 3 . Calculate the material’s bulk modulus.
Solution
The formula for bulk modulus is:
Given:
ΔP = 2.0 x 10 6 Pa
ΔV = 1.0 x 10 -4 m 3
V 0 = 5.0 x 10 -3 m 3
Substituting the values:
The negative sign reflects a reduction in volume. However, the bulk modulus is conventionally expressed as a positive value. Therefore, the bulk modulus of the material is 100 GPa .
Problem 2 : A gas in a sealed container has an initial volume of 0.3 m³. When the pressure is increased by 1.5 x 10 5 Pa, the volume decreases by 0.01 m 3 . Find the bulk modulus of the gas.
Solution
Given:
ΔP = 1.5 x 10 5 Pa
ΔV = 0.01 m 3 = 1.0 x 10 -2 m 3
V = 0.3 m 3 = 3.0 x 10 -1 m 3
The bulk modulus formula is:
Substituting the values:
The negative sign reflects a reduction in volume. However, the bulk modulus is conventionally expressed as a positive value. Therefore, the bulk modulus of the gas is 4.5 GPa .
- References Bulk Modulus – Eng.libretexts.org Bulk Elastic Properties – Hyperphysics.phy-astr.gsu.edu What is Bulk Modulus? – Thoughtco.com Bulk Modulus – App.jove.com
Article was last reviewed on Tuesday, June 10, 2025
