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Chapter 2: Problem 10

The deepest known spot in the oceans is the Challenger Deep in the Mariana Trench of the Pacific Ocean and is approximately \(11,000 \mathrm{m}\) below the surface. For a surface density of \(1030 \mathrm{kg} / \mathrm{m}^{3},\) a constant water temperature, and an isothermal bulk modulus of elasticity of \(2.3 \times 10^{9} \mathrm{N} / \mathrm{m}^{2},\) find the pressure at this depth.

Short Answer

Expert verified
The pressure at the Challenger Deep in the Mariana Trench is approximately \(1.11 * 10^8 Pa\).

Step by step solution

01

Recognition of Given Parameters

The first step involves identifying the data that is given in the problem. The depth \(h\) is \(11000 m\), the density \(\rho\) is \(1030 kg/m^3\), and the gravitational acceleration \(g\) is \(9.81 m/s^2\).
02

Substitution into Pressure Equation

Substitute all known parameters into the pressure formula: Pressure = \(\rho * g * h\). Making this substitution gives: Pressure = \(1030 kg/m^3 * 9.81 m/s^2 * 11000 m\)
03

Compute Pressure

After substitution, compute the Pressure by multiplying \(1030 kg/m^3, 9.81 m/s^2, and 11000 m\). This results in a pressure of about \(1.11 * 10^8 Pa\) (Pascals).

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