B$4.$ An engineer claims that he has built one of the most efficient heat engines, operating

between $1500$C and $400$C$.$

$($a$)$ What is its maximum theoretical efficiency? $(2$ marks$)$

$($b$)$ The actual efficiency of the engine is only $45\mathrm{.}0\%.$ How much mechanical power

does the engine deliver if it discards $1\mathrm{.}00105$ J of energy per second to its cold

reservoir?