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10^(-6)m^(3) volume of water is taken fr...

`10^(-6)m^(3)` volume of water is taken from the surface to the bottom of a lake to a depth of 200 m inside the lake. If the bulk modulus of elasticity of water is 220 atm., then what will be the change in its volume? (Density of water `=10^(3)kgm^(-3))`

Text Solution

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`V=10^(-6)m h=200m, K=220atm`
`P_(e)=h rho g=200xx10^(3)xx9.8=19.6xx10^(5)Nm^(-2)`
i.e. `P_(e)=(19.6xx10^(5))/(1.013xx10^(5))=19.348atm`
`DeltaP=P_(2)-P_(1)=h rho g =19.348atm`
But `K=(- Delta PV)/(DeltaV)`
i.e. `DeltaV=(-(DeltaP)V)/K=(-19.348xx10^(-6))/220=-0.0879xx10^(-6)m^(3)`
`Delta V=-8.79xx10^(-8)m^(3)`
i.e. Decrease in the volume will be `879xx10^(-8)m^(3)`
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