(1) Consider the following charge conservation equation for an electrode, with boundary conditions and deff x2 = a,Fj, (0,t) = 0 os iapp (L,t) = Jeff A where app and A are the applied current and the area of the electrode. By integrating the charge conservation equation, determine the relationship between the input current app (t) and the average lithium flux given by L 1 Javg (x, t)dr. (2) Consider diffusion in a spherical particle governed by 2 OCs = Ds + t 2 r r with boundary conditions and (0,t) = 0, r (R,t) = r DS 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, Hints R 1 Cg= Cs (r,t)dV. 4 The volume of a sphere with a radius r is V = The area of a sphere with a radius r is A = r and hence the infinitesimal volume dV = 4r dr.