#$20\mathrm{.}30$ :: $$As a budding mechanical engineer, you are called upon to design a Carnot engine that has $2\mathrm{.}00$ mol of a monatomic ideal gas as its working substance and operates from a high$-$temperature reservoir at $500$C$.$ The engine is to lift a $15\mathrm{.}0$ kg weight $2\mathrm{.}00$ m per cycle, using $500$ J of heat input. The gas in the engine chamber can have a minimum volume of $5\mathrm{.}00$ L during the cycle.

$($f$)$ What is the maximum volume that the gas chamber will have?