Uranium Diffusion and Decay
Hi, I have the following problem and I am stuck in question 2. I would really appreciate it if you could check that the answer to question 1 is OK, and if you could also give me a hand with question 2.
"A tank of volume 2 , filled with water, is separated into two compartments and of identical volume by a semi-permeable membrane. Uranium is introduced into compartment at a constant mass rate . Uranium is exchanged between compartments and through the membrane at a rate given by , where and are the concentrations of Uranium in each compartment, and is a constant. Because Uranium is radioactive, its mass in each compartment also decays, at a rate proportional to mass, with proportionality constant .
Let and be the masses of Uranium in compartments and . Assume that there is no Uranium in the tank at , that is, , and that the water in each compartment is well mixed.
1.- Write down the differential equations for and describing their evolution.
2.- Find the masses at equilibrium."
So for the first one I have:
Is it correct? What about the second question, how do I work that out? Thanks!