Refrigeration COP Formula
Coefficient of Performance for refrigerators and heat pumps: COP = Q_c/W.
How to measure cooling efficiency with worked examples.
The Formula
COP_heat pump = Q_h / W
The Coefficient of Performance (COP) measures how effectively a refrigerator or heat pump moves heat relative to the work it consumes. Unlike a heat engine (where efficiency is always less than 1), a refrigerator COP can be greater than 1 — you can move more heat than the work you put in.
A refrigerator removes heat Q_c from the cold space (the inside of the fridge) and dumps Q_h into the room, consuming work W from electricity. By energy conservation: Q_h = Q_c + W.
For a heat pump warming a building, we care about Q_h delivered, so COP_hp = Q_h/W. A modern heat pump with COP = 3 delivers 3 kWh of heat for every 1 kWh of electricity — far more efficient than direct electric resistance heating (COP = 1).
The maximum possible COP (Carnot COP) for a refrigerator is: COP_Carnot = T_c / (T_h − T_c), temperatures in Kelvin. A home refrigerator (inside 4°C = 277 K, room 25°C = 298 K) has Carnot COP = 277/21 ≈ 13.2. Real fridges achieve COP of 2–4 due to irreversibilities.
Air conditioners are rated by SEER (Seasonal Energy Efficiency Ratio) in the US, which relates to COP. A SEER 16 unit corresponds to approximately COP 4.7.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| COP | Coefficient of Performance | Dimensionless |
| Q_c | Heat removed from cold reservoir | Joules (J) |
| Q_h | Heat delivered to hot reservoir | Joules (J) |
| W | Work (electricity) consumed | Joules (J) |
Example 1
A refrigerator consumes 150 W and removes 400 W of heat from the food compartment.
COP = Q_c / W = 400 / 150
COP = 2.67 (removes 2.67 J of heat per joule of electricity)
Example 2
A heat pump uses 1 kW of electricity to deliver 3.5 kW of heat to a building.
COP_hp = Q_h / W = 3.5 / 1.0
COP = 3.5 (delivers 3.5 kWh of heat per kWh of electricity)
When to Use It
- Comparing refrigerator and air conditioner models
- Evaluating heat pump economics vs. gas heating
- HVAC system design and energy auditing
- Thermodynamics coursework on reverse cycles