A small house that is 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 electric heat. The heat pump is driven by a 2.5-kW motor, and it has a COP that is one-fourth that of a Carnot heat pump unit. Find the actual COP for the heat pump and the amount of electric heat that must be used (if any) to maintain the house temperature.
Solution 85 HP
Step 1 of 7</p>
We are required to coefficient of performance of heat pump and the amount of electric heat.
Step 2 of 7</p>
Temperature at which the house to be maintained, K
Temperature of the outside ambient,K
Power input of heat pump is, kW
Step 3 of 7</p>
The coefficient of performance of actual pump is given by
Step 4 of 7</p>
The coefficient of performance of is given by