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 x 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. ( 1Pa - 1 Nm^-2)

Answer 1

Given: 

V_i = 100 litre

V_f = 100.5 litre

Change in volume,

ΔV = V_f - V_i = 100.5 - 100 = 0.5 litre

Volumetric strain = ΔV/V_i = 0.5/100 = 5 x 10^-3

Pressure increase, p = 100.0 atm = 100 x 1.013 x 10⁵ Pa

= 1.013 x 10⁷ Pa

Bulk modulus, K = p/(ΔV/V_i) = 1.013 x 10⁷/5 x 10^-3 = 2.026 x 10⁹ Pa