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Use the separation of variables method to solve the following problem. Consider a long, narrow tube...

Use the separation of variables method to solve the following problem. Consider a long, narrow

tube connecting two large, well-mixed reservoirs containing a small concentration of N2 in another

inert gas. The tube length is L = 100 cm. To establish an initial concentration profile in the

tube, each reservoir is held at a fixed concentration: Reservoir 1 contains no N2 and reservoir 2 has

2 × 10−6 mol/cm3 of N2.

(a) At t = 0, the concentrations of the reservoirs are rapidly (instantaneously) switched. Solve

for the concentration in the tube as a function of position and time. The diffusion coefficient of N2

is D = 0.2 cm2/s.

(b) Plot the concentration c(z, t) as a function of the position along the tube at four different

times (initial, early, intermediate, and long times). Use software to plot enough terms of the series

solution to have a reasonable representation of the solution. As always, be sure to clearly label

your axes.

(c) Repeat part (b), but plot the transient part of the solution, ct(z, t).

Expert Solution

c)

Amanda K answered 2 years ago

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