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,
`Delta P` = 100.0 atm, `Delta V` = 0.5 litre
Bulk modulus `B_w = (Delta P xx V)/(Delta V)`
` = (100 xx 100)/(0.5) = 2 xx 10^4 atm`
`B_w = (2 xx 10^4) (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) = (2.026 xx 10^9)/(1.013 xx 10^5) = 2 xx 10^4`
This large ratio suggests that whereas gases are highly compressible, liquids are almost incompressible.