Heat flows naturally from hot to cold. A cup of chai cools down in a room; it never heats itself up. To make heat flow the other way, "uphill", we must spend work. A water pump does the same for water: it lifts water from a sump to an overhead tank.

Your home fridge is a heat pump. It pulls heat out of the food and throws it out at the back grille. Touch that grille and you feel the heat. A water heating heat pump does the same job, but we keep the warm side and use it.

Air at 25 °C in Chennai still holds a lot of heat. Even air at 0 °C in Shimla holds heat, because "cold" only means "less heat". The heat pump collects this low-grade heat and lifts it to a useful temperature, such as 55 °C for bathing water.

Coefficient of performance (COP) is the useful heat delivered divided by the electricity used. An electric geyser element has a COP of about 1. A heat pump typically delivers a COP of 3 to 5 for water heating.

Worked example — heating 500 L of water in Pune from 25 °C to 55 °C.

• Mass of water m = 500 kg. Specific heat c_p = 4.186 kJ/kg·K. ΔT = 55 − 25 = 30 K.
• Q = 500 × 4.186 × 30 = 62,790 kJ. Divide by 3,600 to get kWh: Q ≈ 17.4 kWh.
• Electric geyser (COP ≈ 1): 17.4 kWh × ₹9/kWh (example rate) ≈ ₹157.
• Heat pump at COP 3.5: 17.4 ÷ 3.5 ≈ 5.0 kWh × ₹9 ≈ ₹45.
• Heat taken free from the air: 17.4 − 5.0 = 12.4 kWh.

Remember

• A heat pump moves heat; it does not create it.
• Heat out = heat from source + electrical work.
• COP = useful heat ÷ electricity used.
• Even cold air contains usable heat.