In one cycle, a heat engine absorbs $1\mathrm{.}73$ kJ from a hot reservoir at $277$C and expels $1\mathrm{.}18$ kJ to a cold reservoir at $27$C$.$

$($a$)$ What is the engine's thermal efficiency $($in percent$)?$

$($b$)$ How much work is done by the engine $($in J$)$ in each cycle?

$($c$)$ What is the engine's power output $($in kW$)$ if each cycle lasts $0\mathrm{.}299$ s$?$