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Chapter 1: 93PP (page 32)

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 about480脳106and that the average volume of a single alveolus is 4.2脳106渭尘3. (The volume of a sphere is43蟺谤3and the area of a sphere isdata-custom-editor="chemistry" A=4蟺谤2.)

1.93If we assume that alveoli are spherical, what is the diameter of a typical alveolus? (a)0.20 mm; (b) 2 mm; (c) 20 mm;(d) 200 mm.

Short Answer

Expert verified

The diameter of a typical alveolus is 0.20 mm.

Step by step solution

01

Given data

Total numbers of alveoli,N=480脳106

Average volume of alveoli,V=4.2脳106渭尘3

02

Introduction

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.

03

Step 3: Find the diameter of a typical alveolus

The volume of a sphere in terms of its radius r is,

V=43蟺谤3

And its diameter,d=2r.

Use the above formula to find the diameter of a typical alveolus by assuming that it is a sphere.

V=43蟺谤34.2脳106渭尘3=43脳3.14脳r3r3=1.003脳106渭尘3r=100渭尘

As known that,

1渭尘=0.001mm

Therefore, the radius will be,

r=100脳0.001mm=0.1mm

Diameter is define as below.

d=2r=2脳0.1mm=0.20mm

Hence, the option (a) is correct.

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