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Question:

The approximate depth of an ocean is 2700 m. The compressibility of water is 45.4 × 10⁻⁹ Pa⁻¹ and density of water is 103 kg/m³. What fractional compression of water will be obtained at the bottom of the ocean?

0.8 × 10⁻⁶

1.4 × 10⁻⁶

1.2 × 10⁻⁶

1.0 × 10⁻⁶

Solution:

Compressibility is given as κ = ΔV/(VΔP)
ΔV = κ × ΔP × V
Substituting values
ΔP = ρgh Pa, κ = 45 × 10⁻⁹ Pa⁻¹
ΔV/V = 45 × 10⁻⁹ × ΔP
ΔV/V = 45 × 10⁻⁹ × 103 × 10 × 2700
ΔV/V = 1.2 × 10⁻⁶