bulk modulus

Meaning: Bulk modulus is the elastic modulus for volume change. Pressure is applied equally from all sides, and B compares that pressure change with the fractional decrease in volume it causes. A large B means a small volume change for a given pressure change. Its reciprocal, 1/B, is the compressibility.

Equation: B = −ΔP / (ΔV/V₀), where B is the bulk modulus (Pa), ΔP is the change in pressure (Pa), ΔV is the change in volume (m³), and V₀ is the original volume (m³). The minus sign makes B positive, because volume falls when pressure rises. For sound in a fluid, v = √(B/ρ), where v is wave speed (m/s) and ρ is density (kg/m³).

On the MCAT: A passage gives a pressure change and a fractional volume change and asks for B, or gives B and asks for the volume change. Another common question asks you to rank materials by how easily they compress. The speed-of-sound relation also appears: at similar density, a larger B gives faster sound. Bulk modulus is often grouped with Young's modulus and the shear modulus.

Common confusion: Students treat a large B as meaning easy to compress. It means the opposite, and compressibility is 1/B. Students also mix it up with Young's modulus, which describes stretching along one axis (tensile stress over strain). Bulk modulus describes uniform pressure and volume strain. Liquids are often called incompressible, but that is an approximation, because their B is large and not infinite.