Mechanical Properties of solids NCERT Solutions Class 11 Physics - Solved Exercise Question 9.12

Question 9.12:

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.

Solution:

Initial volume, V₁ = 100.0l = 100.0 × 10 ^–3 m³
Final volume, V₂ = 100.5 l = 100.5 ×10 ^–3 m³
Increase in volume, ΔV = V₂ – V₁ = 0.5 × 10^–3 m³
Increase in pressure, Δp = 100.0 atm = 100 × 1.013 × 10⁵ Pa
Bulk modulus = Δp / (ΔV/V₁)  =  Δp X V₁ / ΔV
= 100 X 1.013 X 10⁵ X 100 X 10^-3 / (0.5 X 10^-3)
= 2.026 X 10⁹ Pa
Bulk modulus of air = 1 X 10⁵ Pa
∴ Bulk modulus of water / Bulk modulus of air  =  2.026 X 10⁹ / (1 X 10⁵)  =  2.026 X 10⁴
This ratio is very high because air is more compressible than water.