$(30$ points$)$

$($a$)(15$ points$)$ A heat engine draws in heat from a boiler and rejects $2$ MW of heat to the surrounding environment. The heat engine's efficiency is rated at $33\%.$ Determine the net power output from the heat engine, and the required heat input from the boiler.

$($b$)(15$ points$)$ A heat pump is found to draw $3$ A of current from a $120$ V receptacle and has a COP of $4\mathrm{.}2.$ Determine the power required to operate the heat pump, and the corresponding amount of heat removed from the cold ambient.

HINT: I strongly suggest you draw diagrams similar to those shown in class, depicting the thermal reservoirs and energy transfers, to better visualize the problem.