A batch reactor contains a liquid solution with reagent A at a concentration of $1$ mol$/$liter at an initial temperature of $25$C$.$ In adiabatic operation of the reactor, what is the time needed to get $60\%$ conversion. The first order reaction, the density and heat capacity throughout the reaction are constant and uniform with values $0\mathrm{.}95$ cal$/$g $$C and $1\mathrm{.}08$ gr$/$cm$3.$ Heat of reaction can be assumed independent of temperature

$(-$Hrxn$)=30$ kcal$/$mol The dependence of the kinetic constant of the process

k$=5\mathrm{.}105$exp$(-10000/$RT$)(mi{n}^{-1})$