1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Modelling DE mixture problem

  1. Aug 14, 2010 #1
    1. The problem statement, all variables and given/known data

    A solution of material A of concentration C0 kg/m3 flows into a tank at the flow rate F m3/min. The tank has fixed volume V m3 and is continuously stirred. The solution on the tank is of concentration C and flows out the top of the tank at the flow rate F. The material A in solution in the tank reacts with air and breaks down such that the amount present in the tank decreases at the rate kCV km/min, where k is constant. At time t=0, the inlet concentration undergoes a step change given by

    C0(t) = Cinit for t<0 and
    C0(t) = C0 for t>0

    a) Write the balance equation for material A in the tank.

    b) Find the solution C(t) of the model. What is the time constant and the limiting concentration in the tank?

    2. Relevant equations

    Rate of change of mass = (rate in) - (rate out)

    3. The attempt at a solution

    d/dt(CV) = C0F - CF - kCV

    dC/dt + (F/V+k)C = FC0/V

    Let CP(t)=A (constant)


    => A=FC0/(F+Vk)

    :. C(t) = FC0/(F+Vk) + me-(F/V+k)t for arbitrary m

    Initially C(0)=FC0/(F+Vk) + m =Cinit


    :. C(t)=FC0/(F+Vk) + (Cinit-FC0/(F+Vk))e-(F/V+k)t, t>0

    As t->infinity, C(t)->FC0/(F+Vk)

    My problem is the very last part, or at least, that's where I noticed I had a problem. Shouldn't the concentration approach C0? Or does the loss of material A into the atmosphere change that?
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted