Cell Mass Balance Equations help

[godiva]

I got a couple questions.

(1) I need to derive reactor volume as a function of time and volumetric flow rate, from the mass conservation equation. I did the following:

. They said it happened in a semi batch reactor so I went further by doing:



I think thats right. Is it?

(2) I need to show that the cell weight in the reactor, can be derived from the cell mass balance equation as a function of mass inflow, volumetric flow rate, μ[sub]m[/sub], and time. They've given the end result which is:



I've worked out from my notes that: N[sub]C[/sub] = XV, N[sub]C[/sub] initially is 0, and F[sub]0[/sub] = X[sub]0[/sub]Q. The hint they gave is to solve the ODE. The thing is I don't know how to express N[sub]C[/sub] as an ODE to evaluate. Any advice please?

(3) Determine the reactor volume after 1 hour given that: V[sub]0[/sub] = 0, Q = 2 L/hr, X[sub]0[/sub] = 0.001 g/Land X[sub]1[/sub] = 0.05 g/L.

Also find μ[sub]m[/sub] assuming that μ[sub]m[/sub] = μ[sub]g[/sub] as the substrate is in excess.

My guess is the answer is obtained from part (1) and (2), or maybe something new entirely? I'm just not sure what to do.


I'm not asking you to do it for me, I've done what I've could, but now I need some help. If you know anything about this, please tell me.