How much pressure (in atm) is is needed to compress a sample of water by 0.4 %?
(Assume, Bulk modulus of water `~~2.0xx10^(9) Pa`)

Options

A. 60 atm
B. 70 atm
C. 80 atm
D. 90 atm

Answer

C

Explanation

Given, percentage change in volume `=0.4 %`
Bulk modulus of water, `B=2xx10^(9) Pa`
The change in volume of water is given by
`Delta V=-(p.V)/B`
where, `p =` pressure applied on the sample of the matter.
Given,
`(Delta V)/(V)=-0.4 %=0.4/100`
Pressure required, `p=B(-(Delta V)/V)`
`=0.4/100xx2xx10^(9) Pa=0.4/100xx(2xx10^(9))/101325` atm
`=79` atm `~~80` atm
Hence, 80 atm pressure is needed to compress a sample of water by 0.4 %