A heat engine operates in a Carnot cycle between $82\mathrm{.}0$C and $345$C$.$ It absorbs $20,000$ J of energy per cycle from the hot reservoir. The duration of each cycle is $5\mathrm{.}00$ s$.$

$($a$)$ What is the mechanical power output of this engine?

kW

$($b$)$ How much energy does it expel in each cycle by heat?

kJ