Providing domestic hot water to a household typically requires 107 kJ of energy per year. A typical electric water heater has an efficiency (heat supplied to water/work input) of 90%, while a heat pump-powered water heater has better performance but is more expensive. The water must be heated to 50 °C and a heat pump would draw heat from the ground at 7 °C. Assume electricity costs $0.08/kWh.
a. Determine the minimum annual operating cost of a heat pump-powered water heater
b. Assume that a heat pump-powered system has an actual coefficient of performance of 2.5 and costs $1000 more than the electric water heater. How many years would it take for the actual heat-pump system to pay off?