A hollow tube 20 cm long is initially filled with air conditioning 4% of ethly alcohol vapors. At the bottom of the tube is a pool of alcohol which evaporates into the stagnant gas above. (Heat transfer from the surroundings to maintain a constant temperature of 25C, at which temperature the vapor pressure is 0.1 atm.) At the upper end of the tube, the alcohol vapors dissipates to the outside air, so the concentration is nearly zero. Considering only the effects of molecular diffusion, determine the concentration of alcohol as a function of time and the distance x measured from the top of the tube. Concentration of ethly alcohol, c, satisfies D = for 0 < x < 20 and t > 0, ax-at x2 with c(x, 0) = 4 and c(0,t) = 0 and c(20,t) = 10 Here D ( = 0 cm 0.15- is the diffusion coefficent of S ethly alcohol into air at 25C, and the vapor pressure is such that the concentration of ethly alcohol at x = 20 cm is 10%. (a) Find an analytical solution for the concentrationdistribution c(x, t) using Laplace Transform, or Fourier Transform or Normal Mode Analysis. (b) Subdivide the length of the tube into 200 intervals. For At 0.01 and 0.04 seconds find the solution using a finite difference method. Employ both explicit and implicit methods for both time steps. Plot c(3,t), c(10, t) and c(16, t) predicted by the explicit and implicit finite difference methods for both time steps and compare these profiles against the results obtained from the analytical solutions. (c) Plot concentration profiles: c(x,5), c(x,25), c(x,150) and c(x,750) obtained either from Analtyical method or Numerical Method.