(2) Consider diffusion in a spherical particle governed by with boundary conditions and əc Ət D₂ acs Ər dcs Ər a²c, 20c + Ər² rər = (0, t) = 0, (R,

t) -2 = 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 ² = — - [² cs(r, t)dV. Hints 4 • The volume of a sphere with a radius r is V = = ³3. • The area of a sphere with a radius r is A = r² and hence the infinitesimal volume dV = 4r²dr.