Question

Compute the bulk modulus of water from the following data: Initial volume = 100.0 litre, Pressure increase = 100.0 atm (1 atm = 1.013 × 105 Pa), Final volume = 100.5 litre. Compare the bulk modulus of water with that of air (at constant temperature). Explain in simple terms why the ratio is so large.

Answer 1

Given,
Initial volume (Vi) = 100 L
final volume (Vf) = 100.5 L
So, increase in volume (∆V) = Vf - Vi = 100.5 - 100 = 0.5 L
= 0.5 × 10^-3 m³

Increase in pressure (∆P) = 100atm = 100× 1.013 × 10^5 N/m² = 1.013 × 10^7 N/m²

Bulk modulus of water (Bw) = ∆P/( ∆V/V)
= 1.013 × 10^7/{0.5 × 10^-3/100×10^-3}
= {10.13/5} × 10^9
= 2.026 × 10^9 N/m²

Bulk modulus of air (Ba)= 1×10^5 N/m²

So, Bulk modulus of water/bulk modulus of air = Bw/Ba = 2.026 × 10^9/10^5 = 2.026×10⁴

Answer 2

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