Compressibility of water is `5 xx 10^(-10) m^(2) N^(-1)`. The change in volume of 100 mL water subjected to `15 xx 10^(6)` Pa pressure will be

Options

A. increases by 0.75 mL
B. decreases by 1.50 mL
C. increases by 1.50 mL
D. decreases by 0.74 mL

Answer

d

Explanation

The reciprocal of bulk modulus B is called compressibility
Since, `B = ("Change in pressure")/("volume strain")`
`implies K = ("Volume strain")/("Change in pressure")`
Given, `K = 5 xx 10^(-10) m^(2) N^(-1), Delta P = 15 xx 10^(6) Pa`
volume strain `= K xx` change in pressure
`:.` volume strain `= 5 xx 10^(-10) xx 15 xx 10^(8)`
`implies` volume strain `= 75 xx 10^(-4) mL`
`(Delta V)/(V) = 75 xx 10^(-4)`
`implies (Delta V)/(100) = 75 xx 10^(-4)`
`implies Delta V = 0.7 mL`
so. decreases in volume by 0.75 mL