An engine absorbs $1\mathrm{.}65$ kJ from a hot reservoir at $277$C and expels $1\mathrm{.}21$ kJ to a cold reservoir at $27$C in each cycle.

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

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

$($c$)$ What is the power output of the engine if each cycle lasts $0\mathrm{.}305$ s$?$