Answer: It will take 11.775 seconds.
Explanation: As a sphere with a diameter of 0.1 mm, the area of an alveolus is
A = 4.π.r²
r for an alveolus would be: r = 0.00005m or r = 5.m
Finding the area:
A = 4.3.14.(5.)²
A = 3.14.m²
The concentration change is to be 90% of the final, so
c = 0.9.3.14.
c = 28.26.
The oxygen diffusivity is 2.4.m²/s, that means in 1 second 2.4.
of oxygen spread in one alveolus area. So:
1 second = 2.4.m²
t seconds = 28.26.m²
t =
t = 11.775s
For a concentration change at the center to be 90%, it will take 11.775s.