Ot $-7$ points total

Q$1$A $(3$ points$)$: A heat engine receives heat from a heat source at $1000C$ and has a thermal efficiency of $45$ percent. The heat engine does maximum work equal to $400$ kJ $.$ Determine the heat supplied to the heat engine by the heat source, the heat rejected to the heat sink, and the temperature of the heat sink.

Q$1$B $(4$ points$)$: The perfornance of a heat pump degrades $($i$.$e$.,$ its COP decreases$)$ as the temperature of the heat source decreases. This makes using heat pumps at locations with severe weather conditions unattractive. Consider a house that is heated and maintained at $22C$ by a heat pump during the winter. What is the maximum COP for this heat pump if heat is extracted from the outdoor air at $($a$)10C($b$)-5C,$ and c