A heat engine operates in a Carnot cycle between $74\mathrm{.}0$C and $345$C$.$ It absorbs $21,200$ J of energy per cycle from the hot reservoir. The duration of each cycle is $2\mathrm{.}00$ s$.$

$($a$)$

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

kW

$($b$)$

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

kJ