$1-(15$ pts$)$ A gas$-$phase, exothermic reaction $AB$ is conducted in two tubular reactors packed with a solid catalyst. Both reactors have the same diameter $($but$,$ not necessarily the same length$)$ and are loaded with the same type of catalyst; however, Reactor $1$ is well$-$insulated and Reactor $2$ includes a heat exchange system that keeps the reactor temperature approximately isothermal.

The reaction follows elementary kinetics. The feed composition, pressure, and flow rate are the same for each reactor, and the same conversion of $70\%$ is achieved in each. It is measured that the outlet pressure for Reactor $2$ is lower than the outlet pressure for Reactor $1.$

With the information given above, can you guess which reactor is longer? Why?