Bulk Modulus
B = −ΔP/(ΔV/V) — cube compresses under hydrostatic pressure. 3D iso visual + live bar.
Key Notes
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.
Formulas
Bulk modulus
Negative sign ensures B > 0 since ΔV < 0 for compressive P.
Compressibility
Fractional volume change per Pa.
Sound speed in a medium
Wave-speed depends on bulk modulus and density.
Ideal gas (isothermal vs adiabatic)
γ = c_p/c_v. Adiabatic bulk modulus governs sound speed in air.
Important Points
Bulk modulus measures volumetric stiffness — solids are nearly incompressible (B ~ 100 GPa).
Sound speed in air ≈ 343 m/s comes from B_S = γP ≈ 1.4 × 10⁵ Pa and ρ ≈ 1.2 kg/m³.
Sound speed in water (~1500 m/s) is fast because B is large despite ρ being moderate.
For a gas: isothermal compression has lower B than adiabatic — that's why sound is approximately adiabatic.
B and Young's Y for the same material are DIFFERENT — Y for stretching, B for compression of all sides.
Compressibility κ is useful in geophysics, fluid mechanics — quantifies how much fluid 'gives' under pressure.
Bulk Modulus notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.