Advertisements
Advertisements
Question
Compute the fractional change in volume of a glass slab, when subjected to a hydraulic pressure of 10 atm.
Advertisements
Solution 1
Hydraulic pressure exerted on the glass slab, p = 10 atm = 10 × 1.013 × 105 Pa
Bulk modulus of glass, B = 37 × 109 Nm–2
Bulk modulus, `B = p/(triangle V/V)`
Where `triangle V/V = p/B`
`=(10xx1.013xx10^5)/(37xx10^9)`
`=2.73 xx 10^(-5)`
Hence, the fractional change in the volume of the glass slab is 2.73 × 10–5.
Solution 2
P = 10 atm = 10 x 1.013 xx 105 Pa; `k = 37 xx 10^9 Nm^(-2)`
Volumetric strain = `(triangleV)/V = P/K = (10xx1.013xx10^5)/(37xx10^9) = 2.74 xx 10^(-5)`
:.Fractional change in volume = `(triangleV)/V = 2.74 xx 10^(-5)`
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?
How much should the pressure on a litre of water be changed to compress it by 0.10%?
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?
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")`
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.
What is the Bulk modulus for a perfect rigid body?
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 gas undergoes a process in which the pressure and volume are related by VPn = constant. The bulk modulus of the gas 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 ______.
Which of the following is an alternate name for bulk modulus?
Compressibility is ______ of the bulk modulus.
Which of the following materials has the highest resistance to compression?
Bulk modulus is defined as the ratio of ______ to ______.
