Consider diffusion in a spherical particle governed by J cs r with boundary conditions and c t = Ds Cs c r cs = r + 2 . 2 (R t) = 3/1/ r r (0, t) = 0, where D, is the diffusion coefficient, R is the radius of the spherical particle. Determine a differential equation for the volume-averaged concentration given by, R 1 = = V Cs (r, t)dV. Hints 4 The volume of a sphere with a radius r is V = r. The area of a sphere with a radius r is A = r and hence the infinitesimal volume dV = 4r dr.