Compute the bulk modulus of water from the following data : initial volume = 100.0 litre, pressure increase = 100.0 atmosphere. Final volume - 100.5 litre . (1 atmosphere = `1.013 xx 10^(5) Pa)`. Compare the bulk modulus of water that of air (at constant temperature). explain in simple terms why the ratio is so large.

Explanation

Initial volume, `V_(1)=100.0l=100.0xx10^(-3)"m"^(3)`
Final volume, `V_(2)=100.5 l=100.5xx10^(-3)"m"^(3)`
Increase in volume, `DeltaV=V_(2)-V_(1)=0.5xx10^(-3)"m"^(3)`
Increase in pressure, `Deltap=100.0atm=100xx1.013xx10^(5)` Pa
Bulk modulus = `((Deltap)/(DeltaV))/(V_(1))=(DeltaPxxV_(1))/(DeltaV)`
`" "=(100xx1.013xx10^(5)xx100xx10^(-3))/(0.5xx10^(-3))`
`" "=2.026xx10^(9)`
Bulk modulus of air = `1.0xx10^(5)` Pa
`therefore("Bulk modulus of water")/("Bulk modulus of air")=(2.026xx10^(9))/(1.0xx10^(5))=2.026xx10^(4)`
This ratio is very high because air is more compressible than water.