3-17. Time to Reach a Steady State in Transient Diffusion In the discussion of the membrane diffusion problem in Section 3.4 it was suggested from order-of-magnitude considerations that a pseudosteady concentration profile would be achieved after a time tL2/D. The objective here is to obtain a more specific estimate of the time to reach a steady state, using the integral approximation method. Assume now that the boundary concentrations, C=KC, at x=0 and C=0 at x=L, are held constant for t0, so that a true steady state will be achieved for t. Let ts be the time required to approach the steady concentration profile to within 5%. (a) During the time period 0tL, a reasonable approximation to the concentration profile is KC0C=a(t)(1)2+(1a(t))(1),=Lx. Remaining to be determined is the function a(t). For consistency with part (a) and with the steady-state solution, what must be the values of a(tL) and a() ? Use this assumed profile to calculate ts