Question

The deepest point in the ocean is 11 km below sea level, deeper than Mt. Everest is tall.

What is the pressure in atmospheres at this depth?

Answer 1

Concepts and reason

The concepts required to solve the given questions is the pressure in the atmosphere at the depth.

Initially, calculate the depth form km to m. Later, write an expression for the pressure at the depth. Finally, calculate the pressure in the atmosphere at this depth.

Fundamentals

The expression for the atmosphere at some depth is as follows:

$P=P^0+Dgh$

Here, $P^0$ is the initial atmospheric pressure, D is the density of water, g is the acceleration due to gravity, and h is the deepest point in the ocean.

The depth in km is equal to,

$h=11\mathrm{k}\mathrm{m}$

Convert it into m as follows:

$\begin{array}{c}h=11\mathrm{k}\mathrm{m}\left(\genfrac{}{}{0ex}{}{{10}^3\mathrm{m}}{1\mathrm{k}\mathrm{m}}\right)\\ =11000\mathrm{m}\end{array}$

Substitute $1.00\mathrm{a}\mathrm{t}\mathrm{m}$for $P^0$, $1030\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$ for D, $9.8\mathrm{m}/{\mathrm{s}}^2$ for g, and 11000 m for h in the equation $P=P^0+Dgh$.

$\begin{array}{c}P=1.00\mathrm{a}\mathrm{t}\mathrm{m}+\left(1030\mathrm{k}\mathrm{g}/{\mathrm{m}}^3\right)\left(9.8\mathrm{m}/{\mathrm{s}}^2\right)\left(11000\mathrm{m}\right)\\ =1.00\mathrm{a}\mathrm{t}\mathrm{m}+1096.09\mathrm{a}\mathrm{t}\mathrm{m}\\ =1097.09\mathrm{a}\mathrm{t}\mathrm{m}\end{array}$

Ans:

The pressure in the atmosphere at the depth is equal to $1097.09\mathrm{a}\mathrm{t}\mathrm{m}$.