Cop Refrigerator⚠ unverified
Physics / Thermodynamics · Compute the coefficient of performance of a refrigerator
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| heat_absorbed | heatabsorbed | J | 1.0 | Heat absorbed from the cold space |
| work_input | workinput | J | 1.0 | Work input to the cycle |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | COP | — | Coefficient of performance (dimensionless). Returns positive infinity if ``work_input`` is not positive |
The science & history
Understanding the Parameters
- $Q_c$ — desired cooling (evaporator heat transfer in).
- $W$ — compressor (and fan) work you pay for; smaller $W$ for same $Q_c$ → better COP.
- COP — e.g. $Q_c = W$ → COP = 1; good domestic units often COP ~ 2–4 depending on conditions. Heat-pump COP heating is $Q_h/W = 1 + Q_c/W$ for the same device (energy balance).
Derivation (Approaching a Proof)
Definition of refrigerator performance: useful cooling per work input,
$$\mathrm{COP}_R \equiv \frac{Q_c}{W}.$$
From the first law for a cycle, $Q_h = Q_c + W$ (magnitudes). Carnot refrigerator limit: $\mathrm{COP}_{R,\mathrm{rev}} = T_c/(T_h - T_c)$.
History
COP is the HVAC and refrigeration industry’s standard efficiency metric; SEER and EER are related seasonal/steady ratings built on the same idea.
Related Concepts: Carnot Efficiency, Thermal Efficiency, First Law DeltaU, Exergy
Notes: Registry calculator cop-refrigerator (unverified). Cooling COP only (not heat-pump
heating COP).