At a given instant a closed system is losing $0\mathrm{.}15$ kW of heat to the outside atmosphere. A battery

inside the system keeps it warm by powering a $0\mathrm{.}15$ kW internal heating lamp. A shaft transfers

$0\mathrm{.}15$ kW of work into the system at the same time. Determine:

$($a$)$ the rate of external work transfer $($include sign$),$

$($b$)$ the rate of heat transfer $($include sign$),$ and

$($c$)$ dE$/$dt of the system.