1. A small house kept at 20?C inside loses 12 kW to the outside ambient at 0?C. A heat pump is used to help heat the house together with possible electrical heat. The heat pump is driven by a motor of 2.5 kW, and it has a COP that is one-quarter that of a Carnot heat pump unit. Find the actual heat pump COP and the exergy destruction in the whole process.
2. A farmer runs a heat pump using 2 kW of power input. It keeps a chicken hatchery at a constant 30?C, while the room loses 10 kW to the colder outside ambient at 10?C. Find the COP of the heat pump, the rate of exergy destruction in the heat pump and its heat exchangers, and the rate of exergy destruction in the heat loss process.