94PP - University Physics with Modern Physics

Question

CALCULATING LUNGS VALUE IN HUMANS. In humans, oxygen and carbon dioxide are exchanged in the blood within many small sacs called alveoli in the lungs. Alveoli provide a large surface area for gas exchange. Recent careful measurements show that the total number of alveoli in a typical pair of lungs is about $\mathbf{480}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}$ and that the average volume of a single alveolus is $\mathbf{4}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}\mathbf{ }{\mathbf{\mu m}}^{\mathbf{3}}$. (The volume of a sphere is $\mathbf{V}\mathbf{=}\frac{\mathbf{4}}{\mathbf{3}}{\mathbf{\pi r}}^{\mathbf{3}}$ and the area of a sphere is $\mathbf{A}\mathbf{=}\mathbf{4}{\mathbf{\pi r}}^{\mathbf{2}}$.) 

 

1.94 Individuals vary considerably in total lung volume.

Figure P1.94 shows the results of measuring the total lung volume and average alveolar volume of six individuals. From these data, what can you infer about the relationship among alveolar size, total lung volume, and number of alveoli per individual? As the total volume of the lungs increases, (a) the number and volume of individual alveoli increase; (b) the number of alveoli increases and the volume of individual alveoli decreases; (c) the volume of the individual alveoli remains constant and the number of alveoli increases; (d) both the number of alveoli and the volume of individual alveoli remain constant.

            

Step-by-Step Solution

Answer

The answer is (b) the number of alveoli increases and the volume of individual alveoli decreases.

Step 1: Given data

Total numbers of alveoli, $\mathrm{N}=480\times {10}^6$ 

 Average volume of alveoli, $\mathrm{V}=4.2\times {10}^6 {\mathrm{\mu m}}^3$  

Step 2: Introduction

The gas exchanging region of the lungs is called alveoli. The product of the total number of alveoli and the average volume of a single alveolus will give the total volume of the alveoli.

Step 3: Find the relationship among them

From the graph, when the total volume of the lungs increases, the average volume of alveoli does not change, since the graph is almost along a horizontal line.

 

According to the graph, the average volume of alveoli does not change, it remains constant as it goes to higher lung volumes.

 

Therefore, option (a), (c) and (d) is incorrect.

 

As the total volume of the lungs increases in the general average volume of 

alveoli decrease.

 

Thus, the number of alveoli will increase.

 

Hence, option (b) is correct.