The maximum allowable temperature for a reactor is $800K.$ At present our operating set

point is $780K,$ the $20-K$ margin of safety to account for fluctuating feed, sluggish controls,

etc. Now, with a more sophisticated control system we would be able to raise our set point to

$792K$ with the same margin of safety that we now have. By how much can the reaction rate,

hence, production rate, be raised by this change if the reaction taking place in the reactor has

an activation energy of $175k\frac{J}{m}ol?$