Insects do not have lungs as we do, nor do they breathe through their mouths. In
ID: 1647750 • 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 1.48 mm long with a cross-sectional area of 1.99 x 10-9m2. The concentration of oxygen in the air outside the insect is 0.633 kg/m3, and the diffusion constant is 1.97 x 10-5 m2/s. If the mass per second of oxygen is diffusing through a trachea is 1.31 x 10-12 kg/s, then find the oxygen concentration at the interior end of the tube.
Explanation / Answer
From the flicks lawof diffusion:
m = D A delta-C t/L
where, D is the diffusion constant, A is the Area, L is the length; Delta-C is the concentrartion difference, t is the time,m is mass
rearranging the abive formula
m/t = D A delta-C/L
delta-C = (m/t)L/ D A
Cout - Cin = (m/t)L/DA
Cin = Cout - (m/t)L/DA
Cin = 0.633 - (1.31 x 10^-12) x 1.48 x 10^-3 / 1.97 x 10^-5 x 1.99 x 10^-9 = 0.585 kg/m^3
Hence, Cin = 0.585 kg/m^3