Refrigerators and Heat Pumps: How They Work and COP

By Engr. Henry Akpan

Making Heat Flow the "Wrong" Way

Heat naturally flows from hot to cold: a cold drink warms up on a hot afternoon, never the reverse. Yet a refrigerator keeps food cold inside a warm kitchen, and an air conditioner pumps heat out of a room into the even hotter air outside. These machines move heat from cold to hot, and the second law of thermodynamics says this can only happen if work is done. This tutorial explains how refrigerators and heat pumps work, the vapour-compression cycle, the coefficient of performance (COP), the Carnot limit, and practical points about air conditioners and energy use. It builds on the tutorials on the first and second laws of thermodynamics.

Refrigerators and Heat Pumps: A Heat Engine in Reverse

A heat engine takes heat Qh from a hot source, turns part of it into work W, and rejects the rest, Qc, to a cold sink. A refrigerator runs this process backwards:

  • it takes in heat Qc from the cold space (the inside of the fridge);
  • it has work W done on it (by an electric motor driving a compressor);
  • it rejects heat Qh to the hot surroundings (the kitchen).

Energy is conserved (the first law), so Qh = Qc + W. The heat dumped into the kitchen is more than the heat taken from the food, which is why the coils at the back of a fridge feel warm. It is also why leaving a fridge door open warms the kitchen rather than cooling it: the fridge just moves heat around the room and adds the motor's work on top.

The Vapour-Compression Cycle

Almost all fridges and air conditioners use a working fluid called a refrigerant, which boils at a low temperature, circulating through four main parts:

  1. Compressor: the motor compresses the refrigerant vapour. Its pressure and temperature rise sharply, so it becomes hotter than the room.
  2. Condenser: the hot vapour flows through coils (behind the fridge, or in the outdoor unit of an air conditioner). It gives out heat Qh to the surroundings and condenses into a liquid, releasing its latent heat.
  3. Expansion valve: the high-pressure liquid passes through a narrow valve. Its pressure drops suddenly and it cools well below the temperature inside the fridge.
  4. Evaporator: the cold, low-pressure liquid flows through coils inside the fridge (or the indoor unit). It absorbs heat Qc from the food or room air and evaporates, taking in latent heat. The vapour then returns to the compressor.

The key physics is latent heat: a liquid absorbs a lot of heat as it evaporates and releases it when it condenses. Changing the pressure changes the boiling point, so the refrigerant can be made to boil in the cold box and condense in the warm room.

Coefficient of Performance of a Refrigerator

For a refrigerator, the useful result is the heat removed from the cold space, and the cost is the work put in. Its performance is measured by the coefficient of performance:

COP(refrigerator) = Qc / W.

Unlike efficiency, the COP is normally greater than 1. A fridge with a COP of 3 removes 3 J of heat from the food for every 1 J of electrical energy used. This doesn't break any law: the fridge is not creating energy, only moving heat that already exists.

Example 1. A refrigerator's compressor uses 100 W and its COP is 3.0. At what rate does it remove heat from the inside, and at what rate does it release heat into the kitchen?

Heat removed = COP × W = 3.0 × 100 = 300 W. Heat released = Qc + W = 300 + 100 = 400 W.

Heat Pumps

A heat pump is the same machine used for the opposite purpose: to heat a building by pumping heat in from the colder outside air or ground. Now the useful output is Qh:

COP(heat pump) = Qh / W = (Qc + W)/W = COP(refrigerator) + 1.

A heat pump with a COP of 4 delivers 4 kW of heat for every 1 kW of electricity, four times as much as an ordinary electric heater, which converts 1 kW of electricity into exactly 1 kW of heat. This is why heat pumps are widely used for heating in cold countries. Many air conditioners are reversible and can run as heat pumps.

The Carnot Limit

The second law sets a maximum possible COP, reached only by an ideal, reversible (Carnot) refrigerator. With temperatures in kelvin:

  • COP(refrigerator, max) = Tc / (Th − Tc)
  • COP(heat pump, max) = Th / (Th − Tc)

Example 2. A fridge keeps its inside at 5 °C (278 K) in a room at 30 °C (303 K). Find its maximum possible COP.

COP(max) = 278 / (303 − 278) = 278/25 ≈ 11.1. Real fridges achieve a COP of perhaps 2 to 4, because of friction, heat leaks, and temperature differences needed to make heat flow through the coils.

Notice the temperature difference in the denominator. The closer Th and Tc are, the easier the job. An air conditioner cooling a room to 24 °C (297 K) when it is 35 °C (308 K) outside has a maximum COP of 297/11 = 27. Setting it to 18 °C makes the difference larger, lowers the COP and raises the electricity bill. Each degree lower on the thermostat typically adds several percent to the energy used.

Air Conditioners in Practice

Air conditioners in Nigeria are often sold by "horsepower" (1 HP, 1.5 HP, 2 HP). This originally described the compressor size; the more useful figure is the cooling capacity, often given in BTU per hour. 1 BTU/h is about 0.293 W, so a 12,000 BTU/h unit (commonly called "1.5 HP") removes about 3.5 kW of heat.

Example 3. A 12,000 BTU/h air conditioner draws 1.1 kW of electrical power. Find its COP.

Cooling capacity = 12,000 × 0.293 ≈ 3,517 W. COP = 3,517 / 1,100 ≈ 3.2. Manufacturers often quote this as the energy efficiency ratio (EER) or, averaged over a season, the SEER.

Running it for 8 hours uses 1.1 kW × 8 h = 8.8 kWh of electricity. An inverter air conditioner, which slows its compressor down instead of switching it fully on and off, often uses noticeably less, and it starts gently, which matters when running from a generator or solar inverter.

Tips for Efficient Cooling

  • Keep the condenser coils clean and well ventilated: if heat can't escape easily, the condensing temperature rises and the COP falls.
  • Don't put hot food straight into a fridge, and keep door openings short.
  • Choose a sensible thermostat setting, such as 24–26 °C for an air conditioner.
  • Insulate and shade rooms so less heat leaks in.

Refrigerants and the Environment

Older refrigerants called CFCs damaged the ozone layer and were phased out under the Montreal Protocol (1987). Their replacements, HFCs, do not harm ozone but are powerful greenhouse gases if they leak, so they are now being phased down too. Newer systems use refrigerants with much lower warming effects, such as R-32, hydrocarbons like R-600a (isobutane) in domestic fridges, and carbon dioxide. Refrigerant should always be recovered by a qualified technician, never vented to the air.

Summary

  • Refrigerators and heat pumps use work to move heat from cold to hot: Qh = Qc + W.
  • The vapour-compression cycle uses evaporation (absorbing latent heat) inside and condensation (releasing it) outside.
  • COP(refrigerator) = Qc/W; COP(heat pump) = Qh/W = COP(refrigerator) + 1. Both are usually greater than 1.
  • The Carnot maximum COP is Tc/(Th − Tc) for cooling; smaller temperature differences mean better performance.
  • Higher thermostat settings, clean coils and good insulation save energy.

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