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Bulk modulus and compressibility

Stress, strain and Hooke's law · Physics

Study notes

A pressure increase of 1.0 × 10⁷ Pa is applied to 2.0 m³ of water (B = 2.2 × 10⁹ Pa). Find the decrease in volume. Step 1: B = −ΔP/(ΔV/V), so ΔV = −V·ΔP/B. Step 2: ΔV = −2.0 × (1.0 × 10⁷) / (2.2 × 10⁹) = −2.0 × 4.545 × 10⁻³ = −9.09 × 10⁻³ m³. Step 3: That is about −9.1 litres out of 2000 litres — less than 0.5%. Answer: The volume decreases by ≈ 9.1 × 10⁻³ m³. Even 100 atmospheres of extra pressure barely squeezes water, showing its huge bulk modulus.

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