Problem $1$

$[25$ points$]$

A $1000-$ liter tank is partially full with $200$ liters of pure water. Beginning at $t=0,$ an aqueous solution containing $2\mathrm{.}0\frac{g}{L}$ of sodium chloride flows into the tank at a flow rate of $10\mathrm{.}0\frac{L}{s}$ and an outlet stream is withdrawn at a flow rate of $5\mathrm{.}0\frac{L}{s}.$ The contents of the tank are perfectly mixed and the density of the feed stream and of the tank solution, $(\frac{g}{L}),$ may be assumed to be constant. The volume of the tank contents and the concentration of sodium chloride in the tank can be represented by $V$ and $C,$ respectively.

a$)$ Draw a schematic diagram of the process and label it with all the known and unknown variables. Identify the initial conditions for $V$ and $C.$

$[04$ points$]$ variables for the process, and develop a mathematical model for the process by applying the appropriate conservation balances to determine the expressions for $V(t)$ and $C(t).$ points