Question # $3(6$ marks$)$

An air conditioning system is used to maintain a house at a constant temperature of of $20C.$ The house is gaining heat from the outdoors at a rate of $20,000k\frac{J}{h}r,$ and the heat generated in the house from people, lights, and appliances amounts to $8000k\frac{J}{h}r.$

A$)$ Sketch a diagram of this process showing hot and cold sinks$,$ the flow of energy and indicating values where given.

B$)$ If the air conditioning system has a $CO{P}_R$ of $2\mathrm{.}5,$ determine the required power input to this air$-$conditioning system. $($Answer in kW $)$

C$)$ If the outside temperature is $35C,$ what is the theoretical maximum $CO{P}_R$ that could be achieved?