A $1$st order, liquid$-$phase, exothermic reaction A$->$B is run in a batch reactor. The reactor is well$-$insulated, so no heat is lost to the surroundings. To control the temperature, an inert liquid C is added to the reaction. The flow rate of C is adjusted to keep T constant at $100\backslash$deg F$.$ What is the flow rate of C after $2$h$?$

TC$0=80\backslash$deg F V$0=50$ ft$3$H$\backslash$deg RX$=-25000$ Btu$/$lb mol

k$(100\backslash$deg F$)=1\mathrm{.}2$ x $10-4$ s$-1$ Cp$,($all components$)=0\mathrm{.}5$ Btu$/$lb mol $\backslash$deg F

CA$0=0\mathrm{.}5$ lb mol$/$ft$3$