Insects do not have lungs as we do, nor do they breathe through their mouths. In
ID: 2294331 • 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 trachea is 1.9 mm long with a cross-sectional area of 2.1 10-9 m2. The concentration of oxygen in the air outside the insect is 0.26 kg/m3, and the diffusion constant is 1.1 10-5 m2/s. If the mass per second of oxygen diffusing through a trachea is 1.7 10-12 kg/s, find the oxygen concentration at the interior end of the tube.
Explanation / Answer
m = [DA(C2-C1)]t/L
where L = .0019 m, D = 1.1 x 10^-5 m^2/s, A = 2.1 x 10 ^ -9 m^2, m = 1.7 x 10 ^-12 kg/s
C1 = .26 kg/m^3 and we are trying to find C2.
This looks like a rate equation if you move 't' to the left side:
m/t = DA(C2-C1)/L
Note that m/t, not m, equals 1.7E-12 kg/s.
Now if C1 is the high concentration I'd think it would be
m/t = DA(C1-C2)/L
Then
m/t*L/(DA) = C1-C2 ==>
C2 = C1-m/t*L/(DA) = 0.26-1.7E-12*0.0019/(1.1E-5*2.1E-9) = 0.120173 kg/m^3