Problem 1 (65) Consider 1-D unsteady diffusion of a dilute molecular species A with concentration, C(x,t), and diffusivity, D, within a slab of thickness b(0xb). At time zero, all moles of A are concentrated at position x=x0 with total amount moles per area equal to N. Molecules of A that reach the boundaries are instantly removed (e.g., by absorption or reaction) such that C(0,t)=C(b,t)=0. a. (40) Show that the time-dependent concentration profile is given by C(x,t)=2bNn=1sin[bnx]sin[bnxo]exp(n22b2Dt) Hint: Express the initial concentration as C(x,t=0)=N(xxo) where (x) is the Dirac delta function, which has the properties, (x)={forx=00forx=0 and ab(xxo)f(x)dx=f(xo) for a