Chapter 1, Problem 37GP

To determine

The average diameter of a single alveolus.

Answer to Problem 37GP

The average diameter of a single alveolus is $\text{2}\text{.34}\times {\text{10}}^{-4}\text{ mm}$ .

Explanation of Solution

Given:

The amount of tiny cavities is $n=300\text{ million}$ .

Formula used:

The expression for the volume of sphere is,

  $V=\frac{4}{3}\pi {\left(\frac{d}{2}\right)}^3$

Here, d is the diameter of the sphere.

Calculation:

Consider the alveoli are in spherical shape and the volume of the alveoli is 2 liters.

The diameter of the single alveolus is calculated using the volume formula.

  $\begin{array}{l}V=\frac{4}{3}\pi {\left(\frac{d}{2}\right)}^3\times n\\ 2\text{ liters}\times \frac{{10}^{-3}{\text{ m}}^3}{1\text{ liter}}=\frac{4}{3}\pi \times {\left(\frac{d}{2}\right)}^3\times \left(300\text{ million}\times \frac{{10}^6}{1\text{ million}}\right)\\ d^3=1.273\times {10}^{-11}\\ d=2.34\times {10}^{-4}\text{ m}\end{array}$

Conclusion:

Thus, the diameter of the single alveolus is $d=2.34\times {10}^{-4}\text{ m}$ .