Advertisements
Advertisements
Question
How much should the pressure on a litre of water be changed to compress it by 0.10%?
Solution 1
Volume of water, V = 1 L
It is given that water is to be compressed by 0.10%.
:.Fractional change, `(triangle V)/V = 0.1/100 xx 1 = 10^(-3)`
`"Bulk modulus", B = rho/((triangle V)/V)`
`p= B xx (triangle V)/V`
Bulk modulus of water, `B = 2.2 xx 10^9 Nm^(-2)`
`p = 2.2 xx 10^(9) xx 10^(-3)`
`= 2.2 xx 10^6 Nm^(-2)`
Therefore, the pressure on water should be 2.2 ×106 Nm–2.
Solution 2
Here `V = 1 "litre" = 10^(-3) m^3; ("ΔV/V") = 0.10/100 = 10^(-3)`
`K = (pV)/(triangle V)`
or `p = k (triangle V)/V = (2.2 xx 10^9) xx 10^(-3) = 2.2 xx 10^6 Pa`
APPEARS IN
RELATED QUESTIONS
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.
What is the density of water at a depth where the pressure is 80.0 atm, given that its density at the surface is 1.03 × 103 kg m–3?
The Marina trench is located in the Pacific Ocean, and at one place it is nearly eleven km beneath the surface of the water. The water pressure at the bottom of the trench is about 1.1 × 108 Pa. A steel ball of initial volume 0.32 m3 is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches to the bottom?
Find the increase in pressure required to decrease the volume of a water sample by 0.01%. Bulk modulus of water = 2.1 × 109 N m−2.
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.
The ratio of adiabatic bulk modulus and isothermal bulk modulus of gas is `("where" γ = "C"_"P"/"C"_"V")`
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.
A gas undergoes a process in which the pressure and volume are related by VPn = constant. The bulk modulus of the gas is ______.
