Advertisements
Advertisements
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.
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 = `((trianglep)/(triangleV))/V_1 = (trianglep xx V_1)/(triangleV)`
`= (100 xx 1.013 xx 10^5 xx 100 xx 10^(-3))/(0.5xx 10^(-3))`
`= 2.026 xx 10^9 Pa`
Bulk modulus of air =`1.0 xx 10^5 Pa`
`:. "Bulk modulus of water"/"Bulk modulus of air" = (2.026 xx 10^9)/(1.0 xx 10^5) = 2.026 xx 10^4`
This ratio is very high because air is more compressible than water.
APPEARS IN
RELATED QUESTIONS
Compute the fractional change in volume of a glass slab, when subjected to a hydraulic pressure of 10 atm.
How much should the pressure on a litre of water be changed to compress it by 0.10%?
Estimate the change in the density of water in ocean at a depth of 400 m below the surface. The density of water at the surface = 1030 kg m−3 and the bulk modulus of water = 2 × 109 N m−2.
Bulk modulus of a perfectly rigid body is ______.
A ball falling in a lake of depth 300 m shows a decrease of 0.3% in its volume at the bottom. What is the bulk modulus of the material of the ball? (g = 10 m/s2)
For an ideal liquid ______.
- the bulk modulus is infinite.
- the bulk modulus is zero.
- the shear modulus is infinite.
- the shear modulus is zero.
To what depth must a rubber ball be taken in deep sea so that its volume is decreased by 0.1%. (The bulk modulus of rubber is 9.8 × 108 Nm–2; and the density of sea water is 103 kg m–3.)
A ball falling in a lake of depth 200 m shows a decrease of 0.1% in its volume. The bulk modulus of elasticity of the material of the ball is ______.
(Take g = 10 m/s2)
The bulk modulus of a liquid is 3 × 1010 Nm-2. The pressure required to reduce the volume of liquid by 2% is ______.
The normal density of a material is ρ and its bulk modulus of elasticity is K. The magnitude of the increase in density of the material, when a pressure P is applied uniformly on all sides, will be ______.
