Chapter 9.5, Problem 35E

Properties of stirred tank solutions

a.    Show that for general positive values of R, V, C_i, and m₀, the solution of the initial value problem

     $\begin{array}{cc}{m}^{\prime }(t)=-\frac{R}{V}m(t)+C_{i}R,& m(0)=m_0\end{array}$

is m(t) = (m₀ – C_iV)e^–Rt/V + C_iV.

b.    Verify that m(0) = m₀.

c.    Evaluate $\underset{t\to \infty }{\lim }m(t)$ and give a physical interpretation of the result.

d.    Suppose m₀ and V are fixed. Describe the effect of increasing R on the graph of the solution.