The first order liquid phase reaction A$$B $($k$=0\mathrm{.}092$ min$-1)$ will be carried out in an isothermal CSTR with the volumetric capacity of $1000$ liters. At the beginning, the reactor is empty and at this time it is started to pump the feed with the rate of $100$ liter$/$min$.$ to the reactor and so the reaction is initiated. The feed contains only A $($no B$)$ with the concentration of CAo $($mole$/$dm$3).$ Unfortunately the pump is out of order after operation of $4$ min. and it takes $10$ min to replace this pump with the new one with the capacity of $50$ liter$/$min$.$ During these operations there is no outlet from the reactor up to filling to complete.

a$.$ What will be the conversion when the reactor is filled up$?$

b$.$ What is the steady state conversion in this reactor?