1. The problem statement, all variables and given/known data Starting from the kinetic equation for the distribution function F*(t, r, v) of some labelled particle admixture in a gas, derive the self-diffusion equation ∂n*/∂t = D∇2n* for the number density n*(t,r) = ∫d3vF*(t,r,v) of the labelled particles. Derive also the expression for the self-diffusion coefficient D. 2. Relevant equations Boltzmann Equation ∂F/∂t + v.∇F = (∂F/dt)c 3. The attempt at a solution Dropping the star notation on n and F ∂n/∂t = ∂/∂t∫Fd3v = ∫∂F/∂t d3v =∫((∂F/∂t)c - v.∇F)d3v (∂F/∂t)c term drops out by definition ( As v is a single vector uniform in space, can write it as ∇φ Therefore ∂n/∂t = ∫∇φ.∇Fd3v Stuck from here on, don't know how to find D either.