What is the density of water at a depth where pressure is 80.0 atm. Given that its density at the surface is 1.03xx10^(3)kgm^(-3)? Compressibility of water is 45.8xx10^(-11)Pa^(-1)

What is the density of water at a depth where pressure is 80.0 atm. Gi

1.	What is the density of water at a depth where pressure is 80.0 atm. Given that its density at the surface is 1.03xx10^(3)kgm^(-3)? Compressibility of water is 45.8xx10^(-11)Pa^(-1)
Answer» SOLUTION :Given density at the surface `=1.03xx10^(3)kgm^(-3)` Compressibility of waer `=45.8xx10^(-11)Pa^(-1)` Bulk Modulus `=1/("compressibility")=1/(45.8xx10^(-11)Pa` `K=2.183xx10^(9)Pa` We know that mass is CONSTANT. As VOLUME changes, density of water changes so that, `(DeltaV)/V=-(Delta rho)/(rho)` but `DeltaP=80-1=79atm=79xx1.013xx10^(5)=80.027xx10^(5)Pa` For compression bulk modulus `K=(-DeltaP)/((DeltaV)/V)` i.e. `K=((DeltaP)/(Delta rho))rho` Change in density `Delta rho=((Delta P)rho)/K=((80.027xx10^(5))(1.03xx10^(3)))/(2.183xx10^(9))` `=37.758xx10^(-1)=3.78kgm^(-3)` Hence density at the depth`=rho + Deltarho` `=1.03xx10^(3)+0.00378xx10^(3)` `=1.03378xx10^(3)` `=rho ' =1.034xx10^(3)kgm^(-3)`