Problem $2(12\mathrm{.}5$ pts$,20$ minutes$)$

A liquid phase irreversible reaction: UlongrightarrowP, takes place in a CSTR of volume $Vr.$ The reactor is initially empty. At $t=0,$ a solution with no reactant flows into the reactor at a constant volumetric flow rate of Fin. No liquid leaves the reactor until the liquid volume reaches a value of $Vr($i$.$e$.$ when reactor is full$).$ When the reactor becomes full at $V_r,$ the exit stream is opened and steady state flow starts at the same time the reactant $U$ is injected to the CSTR and the $l^{st}$ order reaction $R=k^{**}Cu$ starts. Assume the reaction takes place under isothermal conditions, with constant thermal and physical properties.

Sketch and label the system. $1$ pt$.$

Derive the relationship for the concentration of species $U$ within the reactor as a function of time. $10pts$

Specify the steady state concentration of species $U\mathrm{.}1\mathrm{.}5$ pts

$$ Please give a solution on a paper