What is the density of ocean water at a depth, where the pressure is 80.0 atm, given that its density at the surface is `1.03 xx 10^(3) kg m^(-3)`? Compressibilty of water `= 45.8 xx 10^(-11) Pa^(-1)`. Given 1 atm. =`1.013 xx 10^(5) Pa`.

Explanation

`K = (Delta P)/((Delta V)/(V)) rArr (Delta V)/(V) = (Delta P)/(K)`
`rArr (Delta V)/(V) = (DeltaP)C (because C = (1)/(K))`
`(Delta V)/(V) = (79xx1.013xx10^(5)) xx (45.8xx10^(-10))`
`= 36.65xx10^(-3)`
but `(Delta V)/(V) = ((m//rho)-(m//rho^(1)))/((m//rho)) = 1 - (rho)/(rho^(1))`
`(rho)/(rho') = 1 - (Delta V)/(V)` or `rho^(1) = (1.03xx10^(3))/(1-36.65xx10^(-3))`
`rho^(1) = (1.03xx10^(3))/(0.964) = 1.07xx10^(3) kg//m^(3)`