A fairly efficient steam turbine engine fired by coal is used to drive an electric generator. The generator operates between $2100$C and $385$C$.$

$($a$)$ Determine the maximum possible efficiency of the engine.

$\%$

$($b$)$ The engine absorbs $1\mathrm{.}10105$ J from the hot reservoir every second. If the actual efficiency of the engine is $37\mathrm{.}3\%,$ determine the mechanical power the engine delivers.

kW