Insects do not have lungs as we do, nor do they breathe through their mouths. In
ID: 1470450 • Letter: I
Question
Insects do not have lungs as we do, nor do they breathe through their mouths. Instead, they have a system of tiny tubes, called tracheae, through which oxygen diffuses into their bodies. The tracheae begin at the surface of the insect's body and penetrate into the interior. Suppose that a tracheae is 1.50 mm long with a cross-sectional area of 1.21 Times 10^9m^2. The concentration of oxygen in the air outside the insect is 0.754 kg/m^3, and the diffusion constant is 1.78 Times 10^-5 m^2/s. If the mass per second of oxygen is diffusing through a trachea is 1.59 Times 10^-12kg/s, then find the oxygen concentration at the interior end of the tube.Number UnitsExplanation / Answer
The oxygen concentration at the interior end of the tube which will be given as :
using an equation, (m / t) = A D (C2 - C1) / L
C2 = C1 - [(m / t) L / D A]
where, C1 = oygen concentration at outer = 0.754 kg/m3
m/t = mass flow rate of oxygen = 1.59 x 10-12 kg/s
L = length of the trachea = 1.5 x 10-3 m
D = diffusion constant = 1.78 x 10-5 m2/s
A = cross-sectional area of trachea = 1.21 x 10-9 m2
inserting all these values in above eq.
C2 = (0.754 kg/m3) - [(1.59 x 10-12 kg/s) (1.5 x 10-3 m) / (1.78 x 10-5 m2/s) (1.21 x 10-9 m2)]
C2 = (0.754 kg/m3) - [(2.38 x 10-15 kg.m/s) / (2.15 x 10-14 m4/s)]
C2 = (0.754 kg/m3) - (1.107 x 10-1 kg/m3)
C2 = 0.643 kg/m3