Coefficient of Performance: what drives efficiency in a vapour-compression system
By DigiEntropy Engineering · 2026-01-10 · 10 min read
COP is the single number that summarises a refrigeration system's thermodynamic efficiency. This post unpacks its definition, explains what the Carnot limit tells us about the maximum possible COP, and shows how real-world deviations from that ideal show up in measured data and simulation results.
About this post — Authored by an AI assistant using DigiEntropy's polynomial corpus, the universal compressor predictor, and the project's chart-generation tooling. Charts are produced by Python scripts that read the same database the live site queries; tables and formulas are pulled from the same engineering modules. Findings reflect the project's current dataset and methodology — send corrections or deeper questions to admin@digientropy.com.
Defining COP
The coefficient of performance (COP) of a refrigeration system is the ratio of useful cooling delivered to the shaft work consumed:
$\text{COP} = \frac{\dot{Q}e}{\dot{W}{comp}}$
where $\dot{Q}e$ is the evaporator cooling capacity (W or kW) and $\dot{W}{comp}$ is the compressor power input (W or kW). Both are measured at the same operating point — the same evaporating temperature, condensing temperature, refrigerant flow rate, and ambient conditions.
A COP of 3.5 means the compressor delivers 3.5 kW of cooling for every 1 kW of power it draws. The condenser then rejects both: the 3.5 kW absorbed in the evaporator plus the 1 kW of compressor work, 4.5 kW in total. COP has no unit. It is usually above 1, because a refrigerator moves heat rather than turning heat into work, but at a very large lift a cooling COP can fall below 1.
For heat pumps the equivalent figure is:
$\text{COP}{HP} = \frac{\dot{Q}{cond}}{\dot{W}{comp}} = \text{COP}{ref} + 1$
because the condenser rejects the absorbed heat plus the compressor work as useful heating.
5.26 - Carnot COP at −10 °C / 40 °C - the hard upper bound
For a typical medium-temperature commercial refrigeration system (evaporation at −10 °C = 263 K, condensation at 40 °C = 313 K) the Carnot COP is 5.26. This is a hard physical limit — no real machine can exceed it without violating the second law of thermodynamics.
40–60 % - of the Carnot limit - what real systems achieve
Real systems achieve roughly 40–60 % of this Carnot limit.
2–3 % - COP lost per kelvin - of extra condensing temperature
For many reciprocating systems, a rule of thumb is roughly 2–3 % COP loss per kelvin of extra condensing temperature.
7 % - more COP, isentropic 0.68 to 0.73 - all else equal
Raising the isentropic efficiency from 0.68 to 0.73 raises the compressor's COP by 0.73 / 0.68, about 7 %, all else equal.
1.49 - system COP once fans count - the compressor COP is 1.83
On a real cold-room circuit in the System Simulator the difference is large: a compressor COP of 1.83 becomes a system COP of 1.49 once the fans are counted.
11 % - from the best fan speeds - on our reference cold-room circuit
…