Insects do not have lungs as we do, nor do they breathe through their mouths. In
ID: 1488242 • 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 1.08 mm long with a cross-sectional area of 1.34 x 10-9m2. The concentration of oxygen in the air outside the insect is 0.728 kg/m3, and the diffusion constant is 1.83 x 10-5 m2/s. If the mass per second of oxygen is diffusing through a trachea is 1.88 x 10-12 kg/s, then find the oxygen concentration at the interior end of the tube.
Explanation / Answer
here,
Length of Trachea, L = 1.08mm = 0.00108 m
Cross sectional Area, A = 1.34 * 10^-9 m^2
Concentration of Oxygen in air, C1 = 0.728 kg/m^3
Diffusion constant, D = 1.83 * 10-5 m^2/s
mass per unit time, m/t = 1.88 * 10^-12 kg/s
From fick law of diffusion we have
m = [DA(C2-C1)]t/L
or
m/t = DA(C2-C1)/L
where
m is mass,
D is the diffusion constant,
A is the area
C concentration
((m/t)*L)/(D*A) = (C2-C1)
C2 = ((m/t)*L)/(D*A) + C1
C2 = ((1.88 * 10^-12)*0.00108)/(1.83 * 10^-5*1.34 * 10^-9) + 0.728
C2 = 0.811 kg/m^3
the oxygen concentration at the interior end of the tube is 0.811 kg/m^3