Chapter 5, Problem 5.115P

Interpretation Introduction

Interpretation:

The expansion factor for scuba diver’s lungs if she ascends rapidly to the surface from a depth of $125\text{ ft}$ without inhaling or exhaling is to be calculated. Also, the safe distance that she could safely ascend without lung rupture is to be calculated.

Concept introduction:

According to Boyle’s law, the volume occupied by the gas is inversely proportional to the pressure at the constant temperature.

The relationship between pressure and volume can be expressed as follows,

$PV=\text{constant}$

Here, $P$ is the pressure and $V$ is the volume.

The relation between the height of the mercury and water to the density of water and mercury is as follows:

  $\frac{h_{{\text{H}}_{\text{2}}\text{O}}}{h_{\text{Hg}}}=\frac{d_{\text{Hg}}}{d_{{\text{H}}_{\text{2}}\text{O}}}$        (1)

Here, $h_{\text{Hg}}$ is the height of the mercury, $h_{{\text{H}}_{\text{2}}\text{O}}$ is the height of the water, $d_{\text{Hg}}$ is the density of the mercury and $d_{{\text{H}}_{\text{2}}\text{O}}$ is the density of water.