$(20$ pts$)$ Air from inside a house enters a steady$-$flow heat exchanger with a volume flow rate of $200\frac{m^3}{m}in$ at $15C,100$kPa and leaves the heat exchanger at $35C.$ This heat exchanger is located inside the air handler of a house heat pump system and receives heat from the heat pump. The heat pump receives heat from air outside the house that acts as a heat source at $10C.$ Assume air has constant specific heats at the values for $300$ K $.$ Assume air has constant specific heats evaluated at $300$ K $.$

$($a$)$ Determine rate of heat supplied to the air in the heat exchanger QH $,$ in kW $.$

$($b$)$ Assuming the air in the heat exchanger acts as a heat sink having an average temperature of $25C,$ determine the minimum power supplied to the heat pump, in kW $.$