Compute the bulk modulus of water from the following staa , Initial volume = 100. 0 litre, Pressure increase = 100.0 atm (1 atm `=1.013xx10^(5)` 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.

Explanation

Given that V = 100.0 litre, `DeltaP=100.0` atm,
`DeltaV=0.5` litre
Bulk modulus
`B_(w)=(DeltaP xx V)/( DeltaV)=(100xx100)/(0.5)`
`=2xx10^(4)` atm
or `B_(w)=(2xx10^(4)) (1.013 xx 10^(5) Pa)=2.026 xx 10^(9)Pa`
Bulk modulus of air at constant temperature , `B_(a)=P`
Clearly, `(B_(w))/(B_(a)) =(2.026xx10^(9))/(1.013xx10^(5)) =2xx10^(4) `
This large ratio suggests that whereas gases are highly compressible, liquids are almost incompressible.