12.3 Heat pump operation and efficiency

Heat Pump Fundamentals

Heat pumps move thermal energy from a cooler source to a warmer sink, which is the opposite direction heat naturally flows. To make this happen, they require work input, just like a refrigerator. The key difference is the goal: a heat pump's useful output is the heat delivered to the warm space, not the heat removed from the cold space.

Working Principle of Heat Pumps

A heat pump cycles a working fluid (refrigerant) through four main stages in a closed loop:

1. Evaporation — The refrigerant enters the evaporator as a cool, low-pressure liquid. It absorbs heat from the low-temperature source (outdoor air, ground, or water), causing it to evaporate into a gas.
2. Compression — The compressor does work on the low-pressure gas, raising both its temperature and pressure significantly. This is where the external work input enters the cycle.
3. Condensation — The hot, high-pressure gas flows through the condenser, where it releases heat to the high-temperature sink (the space you're heating). As it loses energy, the refrigerant condenses back into a liquid.
4. Expansion — The liquid refrigerant passes through an expansion valve, which drops its pressure and temperature sharply. The cool, low-pressure fluid then returns to the evaporator, and the cycle repeats.

Heat Pumps vs. Refrigeration Cycles

Heat pumps and refrigerators share the same four components (compressor, condenser, expansion valve, evaporator) and operate on the same thermodynamic cycle. The difference is which energy transfer you care about:

Because of this, the condenser is the "business end" of a heat pump, while the evaporator is the "business end" of a refrigerator.

Heat Pump Performance and Applications

Coefficient of Performance for Heat Pumps

The coefficient of performance (COP) measures how effectively a heat pump converts work input into delivered heat:

$COP_{HP} = \frac{Q_H}{W_{input}}$

where $Q_H$ is the heat delivered to the warm space and $W_{input}$ is the work supplied to the compressor.

A COP of 3, for example, means the heat pump delivers 3 kJ of heat for every 1 kJ of electrical work consumed. This is possible because the pump isn't creating heat; it's moving heat from the source and adding the compressor work on top. By the first law applied to the cycle:

$Q_H = Q_L + W_{input}$

so the COP can also be written as:

$COP_{HP} = \frac{Q_H}{Q_H - Q_L}$

For an ideal (Carnot) heat pump operating between a cold reservoir at $T_L$ and a hot reservoir at $T_H$ (both in Kelvin):

$COP_{HP,\text{Carnot}} = \frac{T_H}{T_H - T_L}$

This is the theoretical maximum. Several factors determine how close a real heat pump gets to this limit:

• Temperature difference between source and sink — A smaller $T_H - T_L$ gives a higher COP. On a mild winter day, your heat pump works more efficiently than during a deep freeze.
• Compressor efficiency — Real compressors have friction and irreversibilities that reduce performance below the Carnot value.
• Refrigerant properties — The refrigerant's boiling point, latent heat, and pressure-temperature relationship all affect how well the cycle performs.
• Heat exchanger effectiveness — Better heat exchangers keep the working fluid temperatures closer to the actual source and sink temperatures, reducing irreversibility.

Applications of Heat Pumps

Space heating is the most common application. Air-source heat pumps extract heat from outdoor air (effective even in cold weather, though COP drops as outdoor temperature falls). Ground-source (geothermal) heat pumps draw from underground, where temperatures stay relatively stable year-round, giving a more consistent COP.

Water heating uses the same principle to heat domestic or commercial water supplies. The heat pump extracts energy from surrounding air, ground, or a water source and transfers it to a storage tank. These systems can be 2–3 times more efficient than conventional electric resistance water heaters.

Industrial processes benefit from heat pumps in two main ways:

• Process heating — Supplying low-to-medium temperature heat for drying, pasteurization, or similar operations.
• Waste heat recovery — Capturing low-grade waste heat from an industrial process and upgrading it to a higher, more useful temperature.

Benefits of Heat Pump Usage

• Energy savings — Because COP values typically range from 2 to 5, heat pumps deliver significantly more thermal energy than the electrical energy they consume. A resistance heater, by comparison, has a COP of exactly 1.
• Reduced emissions — Heat pumps powered by electricity produce no on-site combustion, eliminating local pollutants. When the electricity grid includes renewables, the overall carbon footprint drops further.
• Lower operating costs — Delivering multiple units of heat per unit of electricity means lower energy bills compared to direct electric or fossil-fuel heating, especially in moderate climates where COP stays high.