At a given instant a closed system is loosing 0.1 kW of heat to the outside atmosphere. A battery inside the system keeps it warm by powering a 0.1 kW internal heating lamp. A shaft transfers 0.1 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.