Bulk Modulus

Bulk modulus B (sometimes K) measures resistance to VOLUME change under hydrostatic pressure.

Definition: B = −P/(ΔV/V). Negative sign because volume DECREASES as pressure INCREASES.

Units: Pa, same as pressure.

Typical values: steel ≈ 160 GPa, water ≈ 2.2 GPa, air ≈ 0.0001 GPa (at 1 atm). Solids are nearly incompressible; gases very compressible.

Compressibility κ = 1/B — fractional volume change per unit pressure.

Bulk modulus determines the speed of sound in fluids and solids: v = √(B/ρ) for longitudinal waves.

For ideal gas: isothermal B_T = P (= 10⁵ Pa at 1 atm); adiabatic B_S = γP.

Solids' bulk modulus is HIGH (~10² GPa) ⇒ they barely change volume even under enormous pressure.