In a Batch Reactor of $5$ m$^3$ volume, the reaction is carried out in the liquid and exothermic phase AB$.$ The reaction speed is$-$TA$=$ k CA with k $4-10$ exp$((-7900/$T$)$ s$1$The initial temperature of the reaction mixture is $20\backslash$deg C and the maximum reaction temperatureAH$=-1670$ kJ$/$kg$,$permissible is $95\backslash$deg C$.$The reactor has a heat exchanger with an area of $3\mathrm{.}3$ m$^2$ that can operate with steam $($T $120\backslash$deg C$,$ U$=1360$ W$/$ m$^2\backslash$deg C$)$ or with cooling water $($T$15\backslash$deg C$,$ U$=1180$ W$/$ m$^2\backslash$deg C$).).$ Theheat exchange rate is given by Q $=$U A AT$=$ M$.$Cp dT$/$dtDetermine the reaction times and total operating time to achieve a conversionXA $0\mathrm{.}9$ for the following two process sequences : a$)$ Preheat up to $55\backslash$deg C$,$ operate adiabatically and cool when T$=95\backslash$deg C is metor that XA $=0\mathrm{.}9$ and then cool to $45\backslash$deg C$.$ b$)$ Heat up to $95\backslash$deg C$,$ operate isothermally up to XA $=0\mathrm{.}9$ and cool down to $45\backslash$deg C Other data:The reactor filling and emptying times are $10$ and $15$ min respectively. The heat capacities for A and B are identical and equal to $4200$ J$/$kg C$.$ The density of both components is $100$ kg$/$m$^3.$ CAo $=1$ kmol$/$ m