A series of two cellulose acetate membranes are used to purify a 15.0 mol% carbon dioxide -85.0 mol% methane stream. The feed rate to the first membrane (1) is 1.0 kmol/hr and the cut, θ1 = 0.2. The permeate stream from the first membrane is sent as feed to the second unit (2) which uses a cut, θ2 = 0.4. Both units operate at the same pressure ratio and can be represented with the same RT curve, given below.
(a) Find the composition of CO2 leaving in the permeate of the second membrane unit, yP2,CO2.

(b) Find the overall % loss of CH4, i.e. % of CH4 fed that leaves in the permeate stream of the second membrane.