Coefficient of Performance Calculator

Calculate COP for refrigerators and heat pumps using actual data or Carnot cycle analysis

Calculate Coefficient of Performance

Heat extracted from cold reservoir

Heat expelled to hot reservoir

Work done on the system (calculated as Qh - Qc if not provided)

COP Results

0.000
COP Refrigerator
Actual Performance
0.0%
Energy Efficiency
Output/Input ratio

Performance Analysis

Example Calculation

Home Refrigerator Example

Heat removed from food compartment: Qc = 150 kJ

Heat rejected to kitchen: Qh = 200 kJ

Work input: W = Qh - Qc = 200 - 150 = 50 kJ

COP Calculation

COPrefrigerator = Qc / W = 150 / 50 = 3.0

COPheat pump = Qh / W = 200 / 50 = 4.0

Energy efficiency: 75% (3.0 out of 4.0 possible)

Typical COP Values

Refrigerators

Food preparation2.6-3.0
Meat/dairy2.3-2.6
Frozen foods1.2-1.5
Ice cream1.0-1.2

Heat Pumps

Air-source~3.0
Geothermal3.0-6.0

Key Principles

First Law

Qh = Qc + W

COP Relationship

COPhp = COPr + 1

Carnot Limit

Maximum theoretical COP

Energy Efficiency

COP > 1 for all practical systems

Understanding Coefficient of Performance

What is COP?

The Coefficient of Performance (COP) is a measure of the efficiency of refrigerators and heat pumps. Unlike traditional efficiency which is always less than 1, COP can be greater than 1 because these devices move heat rather than convert energy.

COP Formulas

Refrigerator:

COPr = Qc / W

Heat removed per work input

Heat Pump:

COPhp = Qh / W

Heat delivered per work input

Carnot COP

The Carnot COP represents the theoretical maximum efficiency achievable for given temperature reservoirs. Real systems always have lower COP than the Carnot limit due to irreversibilities.

Carnot Refrigerator:

COPr,rev = Tc / (Th - Tc)

Carnot Heat Pump:

COPhp,rev = Th / (Th - Tc)

Note: Use absolute temperatures (K or °R) for Carnot calculations