In household water heating, conventional electric immersion heaters heat the water directly using electrical resistance. Air-source heat pump water heaters use a compression cycle to transfer heat from the surrounding air to the water.
A conventional immersion heater requires about 4.0 kWh4.0\text{ kWh}4.0 kWh of electrical energy to heat a tank of water. An air-source heat pump system requires only about 1.3 kWh1.3\text{ kWh}1.3 kWh of electrical energy to heat the same volume of water to the same temperature.
Explain why the heat pump system uses less electrical energy than the conventional immersion heater.
The hot water in the cylinder is maintained at a temperature of 60 ∘C60\text{ }^\circ\text{C}60 ∘C. The heat pump can draw thermal energy from either a utility room at 21 ∘C21\text{ }^\circ\text{C}21 ∘C or from the outside air at 2 ∘C2\text{ }^\circ\text{C}2 ∘C.
Deduce which of these two environments results in lower running costs for the heat pump water heater. Support your answer with calculations of the maximum thermodynamic efficiency (coefficient of performance).
