Question

How much should the pressure on a litre of water be changed to compress it by 0.10%? Bulk modulus of elasticity of water = `2.2 xx 10^(9) Nm^(-2)`.

Answer 1

Volume of water, V = 1 L
It is given that water is to be compressed by 0.10%.
`therefore"Fractional change",(DeltaV)/(V)=(0.1)/(100xx1)=10^(-3)`
Bulk modulus, `B=((rho)/(DeltaV))/(V)`
`p=Bxx(DeltaV)/(V)`
Bulk modulus of water, `B=2.2xx10^(9)"Nm"^(-2)`
`p=2.2xx10^(9)xx10^(-1)`
`=2.2xx10^(6)"Nm"^(-2)`
Therefore, the pressure on water should be `=2.2xx10^(6)"Nm"^(-2)`.