3. Gaseous Diffusion of Species A Through Stagnant B in a Tube of Variable Cross-Section (50 pts) In lecture on Friday Jan. 27, we discussed gaseous diffusion of species A in a tube of variable cross section in which the radius of the tube increases linearly with distance z down the tube. See those lecture notes for a diagram of the problem, or Figure 19.1-3 (b). We discussed that an enhancement in the diffusion rate is expected for a diffusion tube in which the radius increases with distance down the tube. For this problem, the equation for the total molar diffusion rate (NA) is equation 19.1-28 in the text NAz1z2[(z2z1r2r1)z+r1]2dz=RTDABPA1PA21PA/PdPA a) Show that the integration of the equation above, and solving for (NA) is NA=a[az1+r11az2+r11]1RTDABPln(PPA1PPA2) Where a=(z2z1r2r1), which is the change in tube radius with distance down the tube, and in which you may use in the integration of the left hand side the integral formula (az+r1)2dz= a1(az+r1)1 to determine NA. The term a[az1+r11az2+r11]1 in the equation above for NA is a geometric term because it contains the parameters that describe the shape of the tube. b) Now, show that for a tube of constant cross section in which r2=rl, you may integrate equation 19.128 to get NA=z2z2r12RTDABPln(PPA1PPA2) The term z2z2r12 in the equation immediately above is also a geometric term for the case of a constant cross section diffusion tube. c) Finally, note that the term RTDABPln(PPA1PPA2) is the same in both cases, and only the geometric terms are different. Therefore, we may determine the enhancement in the diffusion rate from the geometric terms alone. For the following values, rI=0.1m,r2=0.2 m,zl=0m, and z2=1m, determine the value of the geometric factor for part a) and also for part b), and then calculate the ratio of the geometric term for a) divided by the term for b ) to determine the enhancement factor for the diffusion rate