Coefficient of Performance (COP) of Refrigeration System: Definition, Formula, and Experiment

What is Coefficient of Performance (COP)?

The Coefficient of Performance (COP) is a measure of the efficiency of a refrigeration or heat pump system. It is the ratio of useful heat energy moved to the work energy input required to move it.

A higher COP means greater efficiency, more cooling or heating is achieved per unit of electrical energy consumed.

COP Formula for Refrigerators

COP_refrigerator = Q_L / W_net

Where:

• Q_L = Heat removed from the cold reservoir (refrigeration effect), kJ
• W_net = Net work input to the compressor, kJ

For a Carnot refrigerator (theoretical maximum):

COP_Carnot = T_L / (T_H – T_L)

Where T_H and T_L are the absolute temperatures (Kelvin) of the hot and cold reservoirs.

COP Formula for Heat Pumps

COP_HP = Q_H / W_net = COP_R + 1

A heat pump always has COP > 1, and COP_HP = COP_R + 1 (where COP_R is the COP of the same system used as a refrigerator).

Vapour Compression Refrigeration Cycle

The standard refrigeration cycle consists of four processes:

1. 1→2: Isentropic Compression, refrigerant compressed in the compressor (work input)
2. 2→3: Condensation, refrigerant rejects heat Q_H at constant pressure in condenser
3. 3→4: Throttling (Expansion), pressure drop through expansion valve (irreversible, no work output)
4. 4→1: Evaporation, refrigerant absorbs heat Q_L at constant pressure in evaporator

P-H Diagram for Refrigeration

The vapour compression cycle is best analysed on a Pressure-Enthalpy (P-H) diagram:

• Refrigerating effect: Q_L = h₁ – h₄ (enthalpy at evaporator outlet minus inlet)
• Compressor work: W = h₂ – h₁
• Heat rejected: Q_H = h₂ – h₃
• COP = Q_L / W = (h₁ – h₄) / (h₂ – h₁)

Factors Affecting COP

Refrigeration Cycle Experiment

Using the Refrigeration Trainer, students:

1. Record temperatures and pressures at all four cycle points
2. Measure compressor power input (kW)
3. Determine enthalpy values from P-H chart for the refrigerant used
4. Calculate actual COP and compare with Carnot COP
5. Draw the actual cycle on the P-H diagram

Scientico India’s refrigeration trainer is available with R-134a or R-410A refrigerant, CE certified and ISO 9001:2015 compliant. Request a quote for your mechanical engineering department.

COP Calculation, Detailed Example with Pressure-Enthalpy Diagram

Standard Vapour Compression Refrigeration Cycle

The vapour compression refrigeration cycle consists of four processes on the p-h (pressure-enthalpy) diagram:

1. 1→2 (Compression): Isentropic compression in compressor. Low-pressure refrigerant vapour is compressed to high pressure. Temperature rises.
2. 2→3 (Condensation): Heat rejection to atmosphere in condenser. High-pressure vapour condenses to liquid at constant pressure.
3. 3→4 (Expansion): Throttling through expansion valve. High-pressure liquid flashes to low-pressure wet vapour at constant enthalpy (h₃ = h₄).
4. 4→1 (Evaporation): Heat absorption from refrigerated space in evaporator. Wet vapour evaporates at constant pressure and temperature.

COP Formula and Calculation

COP = Refrigerating effect / Work input = (h₁ – h₄) / (h₂ – h₁)

where h₁, h₂, h₃, h₄ are enthalpies at states 1, 2, 3, 4 respectively.

Sample Calculation (R-134a at Typical Lab Conditions)

Evaporator temperature: -10°C → Evaporator pressure ≈ 2.0 bar
Condenser temperature: 40°C → Condenser pressure ≈ 10.2 bar

From R-134a tables:
h₁ = 392.4 kJ/kg (saturated vapour at -10°C)
h₂ = 430.5 kJ/kg (superheated at 10.2 bar, after isentropic compression)
h₃ = 256.5 kJ/kg (saturated liquid at 40°C)
h₄ = h₃ = 256.5 kJ/kg (throttling, constant enthalpy)

Refrigerating effect = h₁ – h₄ = 392.4 – 256.5 = 135.9 kJ/kg

Work input = h₂ – h₁ = 430.5 – 392.4 = 38.1 kJ/kg

COP_actual = 135.9/38.1 = 3.57

COP_Carnot = T_L/(T_H – T_L) = 263/(313-263) = 5.26

Refrigerating efficiency = COP_actual / COP_Carnot = 3.57/5.26 = 67.9%

Factors Affecting COP

• Higher evaporator temperature → higher COP
• Lower condenser temperature → higher COP
• Superheating at compressor inlet → slight improvement (drier compression)
• Subcooling at condenser exit → increases refrigerating effect → improves COP
• Compressor efficiency (mechanical and volumetric) → lower actual COP than ideal