Compute the bulk modulus of water from the following data : Initial volume =100.0 litre, pressure increase=100.0 atm `(1atm=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

Here, `V=100lit=100xx10^(-3)m^(3),P=100`
`atm=100xx1.013xx10^(5_Pa`
`V+DeltaV=100.5` litre or `DeltaV=(V+DeltaV)-V`
`=100.5-100`
`=0.5` litre `=0.5xx10^(-3)m^(3)`
We know that bulk modulus, `B=(PV)/(DeltaV)`
`=(100xx1.013xx10^(5)xx100xx10^(-3))/(0.5xx10^(-3))`
`=2.026xx10^(9)Pa`
Bulk modulus of air=`1.0xx10^(5)Pa`
Bulk modulus of water `2.026xx10^(9)`
Bulk modulus of air `=1.0xx10^(5)`
`=2.026xx10^(14)`
It is so because gases are much more compressible than those of liquids. the molecules in gases are very poorly coupled to their neighbours as compared to those of gases.