Thermodynamics
Coefficient of Performance (Refrigerator)
Performance metric for refrigerators.
Variables
COPRunitless
COP (refrigerator)
Cooling per work
Allowed values: greater than 0
QCJ
Heat removed
Heat from cold reservoir
In SI units: kg·m²/s²
Allowed values: greater than 0
WJ
Work input
Work required
In SI units: kg·m²/s²
TCK
Cold temperature
Cold reservoir temp
Allowed values: greater than 0
THK
Hot temperature
Hot reservoir temp
Allowed values: greater than 0
Derivation
COP = Q_C/W. For Carnot: COP = T_C/(T_H - T_C).
Your notes
0/5000
Check value
Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.
- QC = 2 J (Heat removed)
- W = 3 J (Work input)
Result: COPR = 0.66666667
Other thermodynamics formulas with the same quantities
- Coefficient of Performance (Heat Pump) (Second Law) shares Work input, Hot temperature, Cold temperature
Where this formula is listed
- Thermodynamics formulas, under Second Law, alongside Entropy Change, Heat Engine Efficiency and Clausius Inequality.
- In the thermodynamics list it comes after Heat Engine Efficiency and before Coefficient of Performance (Heat Pump).
- Thermodynamics formula sheet, one of 34 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Coefficient of Performance (Refrigerator) formula?
Coefficient of Performance (Refrigerator) is written COP_R = Q_C/W = T_C/(T_H − T_C). Performance metric for refrigerators. It belongs to Thermodynamics, under Second Law.
What are the units in COP_R = Q_C/W = T_C/(T_H − T_C)?
In SI units, COP_R is cop (refrigerator) (dimensionless); Q_C is heat removed, measured in kg·m²/s²; W is work input, measured in kg·m²/s²; T_C is cold temperature, measured in K; T_H is hot temperature, measured in K.
How is the Coefficient of Performance (Refrigerator) formula derived?
COP = Q_C/W. For Carnot: COP = T_C/(T_H - T_C). The result is COP_R = Q_C/W = T_C/(T_H − T_C).