5.The rubber tube of a bicycle tyre is inflated to an absolute pressure P?. Considering that the
loss of pressure with time is due to the diffusion of N? and O? through the rubber tube, show
that the time it takes for the pressure to reduce to P? is given by the following equation,
assuming that the diffusion follows Fick's law with a linear profile through the tube wall and
an effective diffusion coefficient D<sub>AB</sub>. The surface area, volume and rubber wall thickness of
the tube are S m², V m³, and w m, respectively. The atmospheric pressure outside the tube
is P<sub>o</sub>.
t = \frac{wV}{SD_{AB}} \ln{\frac{P_1 - P_o}{P_2 - P_o}}
6. Use the equation of Question 5 to calculate the diffusion coefficient of the rubber tube if
the pressure in the tube is reduced from 3 bar to 2 bar in six months time, taking the
atmospheric pressure as 1 bar. The diameter of the cross-sctional area of the tube is 50 mm,
and if the tube is cut, the length of the tube, approximating it to a cylinder, is 1.8 m. The
tube thickness is 1 mm.