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
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
Heat Pumps
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