Question

What is the density of ocean water at a depth, where the pressure is $80.0 \mathrm{~atm}$, given that its density at the surface is $1.03 \times 10^{3} \mathrm{kgm}^{-3}$ (compressiblility of water $=45.8 \times 10^{-11} \mathrm{~Pa}^{-1}$ )?

   What is the density of ocean water at a depth, where the pressure is $80.0 \mathrm{~atm}$, given that its density at the surface is $1.03 \times 10^{3} \mathrm{kgm}^{-3}$ (compressiblility of water $=45.8 \times 10^{-11} \mathrm{~Pa}^{-1}$ )?

Practice Problem in Physics for the JEE Main and Advanced

Abhay Kumar 2015 Edition

Chapter 9, Problem 5

Instant Answer

Solved by Expert Hast Aggarwal

01/17/2022

Step 1

Step 1: The density of a fluid under pressure can be calculated using the formula: \[ \rho = \rho_0 / (1 - \beta P) \] where: - $\rho$ is the density of the fluid under pressure, - $\rho_0$ is the initial density of the fluid (at the surface), - $\beta$ is Show more…

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What is the density of ocean water at a depth, where the pressure is $80.0 \mathrm{~atm}$, given that its density at the surface is $1.03 \times 10^{3} \mathrm{kgm}^{-3}$ (compressiblility of water $=45.8 \times 10^{-11} \mathrm{~Pa}^{-1}$ )?

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Key Concepts

Compressibility

Compressibility is a property of a material that quantifies how much its volume changes in response to a change in pressure. It is defined as the fractional change in volume per unit increase in pressure. In the context of fluids like water, a small compressibility value indicates that the fluid is nearly incompressible, meaning that significant pressure changes lead to only small changes in volume and, correspondingly, density.

Pressure Effects on Fluid Density

Pressure has a direct effect on the density of a fluid. When pressure increases, the fluid is compressed and its density increases because the same mass of fluid occupies a slightly reduced volume. This relationship between pressure, compressibility, and density allows us to calculate the variation in density with depth in the ocean using the compressibility of water and the initial conditions at the surface.

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