a family wishes to purchase a heat pump for their home. The get-it-cheap co. sells a heat pump that has an operating performance 38% of the coefficient of performance of an ideal Carnot heat pump. The price is $3200. For $5200, the Top-of-the-line Co. sells a heat pump that has an operating performance 52% of that of an ideal Carnot heat pump. The family wishes to maintain their home at 21C with an average winter outside temperature of -5C. The family estimates that it will take an average of 21 GJ of energy per month to keep the house heated to this temperature for 5 cold months. The cost of electrical energy is $0.0185/kWh.
1. Compute the overall coefficient of performance for each heat pump.
2. Compute the cost of running each heat pump for 5 cold months.
3. How long will it take for the top-of-the-line heat pump to make up the cost differential?