How to calculate the COP of the vapor-compression refrigeration cycle lets you estimate the coefficient of performance (COP) of refrigerators, air conditioners and heat pumps. The cycle is the backbone of modern refrigeration: Willis Carrier patented the first AC unit in 1902 (Buffalo NY), and today 1.6 billion AC units operate worldwide. The 4-phase cycle: adiabatic compression of vapor (1→2), isobaric condensation with Q_H release (2→3), isenthalpic throttling through expansion valve (3→4), isobaric evaporation with Q_L absorption (4→1). Refrigeration COP: COP_R = Q_L/W = (h_1-h_4)/(h_2-h_1). Heat pump COP: COP_HP = Q_H/W = COP_R + 1. Carnot limit: COP_Carnot = T_L/(T_H-T_L). Modern refrigerants: R-134a (HFC, GWP 1430), R-410A (blend, GWP 2088), R-32 (HFC, GWP 675), R-744 (CO₂, GWP 1, transcritical), R-290 (propane, GWP 3). EU F-Gas Regulation 517/2014 and 2024/573 mandates HFC phase-down. Manufacturers: Daikin (Japan), Mitsubishi Electric, Carrier (USA), Trane Technologies, Johnson Controls.

1. Vapor-compression cycle explained

The vapor-compression cycle is the most widespread refrigeration cycle: it transfers heat from a cold reservoir (T_L, evaporator) to a hot one (T_H, condenser) via mechanical work W (compressor). The 4 transformations: (1→

• adiabatic compression of saturated vapor in compressor (W = h_2-h_1); (2→
• isobaric condensation in condenser with Q_H = h_2-h_3 release; (3→
• isenthalpic throttling in expansion valve (h_3=h_4); (4→

1) isobaric evaporation in evaporator with Q_L = h_1-h_4 absorption. COP_R = Q_L/W = (h_1-h_4)/(h_2-h_1). Enthalpies h read from p-h Mollier diagrams or from refrigerant equations of state (REFPROP NIST, CoolProp open-source).

2. Modern refrigerants and regulations

• R-134a (1,1,1,2-tetrafluoroethane) — HFC, GWP 1430, ODP 0, EU F-Gas phase-down.
• R-410A — R-32+R-125 blend, GWP 2088, residential AC, phase-out 2025.
• R-32 (difluoromethane) — HFC, GWP 675, A2L mildly flammable, R-410A replacement.
• R-744 (CO₂) — natural, GWP 1, transcritical for high-T heat pumps (Eco-Cute).
• R-290 (propane) — natural, GWP 3, A3 flammable, commercial AC.
• R-1234yf, R-1234ze — 4th-generation HFO, GWP <1, automotive (BMW, Mercedes).
• R-717 (NH₃) — natural, GWP 0, large industrial plants (cold storage).
• R-600a (isobutane) — domestic refrigerators Bosch, Whirlpool, Liebherr.

3. Validity range and real corrections

COP_Carnot is the thermodynamic maximum: COP_Carnot = T_L/(T_H-T_L). For T_L=273 K (0°C), T_H=313 K (40°C): COP_Carnot=6.8. Real COP 2.5-4.5 for residential AC (R-410A), 1.8-3.5 for air-water heat pumps, 4-7 for geothermal heat pumps (CIAT, Stiebel Eltron). Losses: (a) non-isentropic compressor (η_isen 0.7-0.85); (b) non-isobaric condenser (5-10% pressure drop); (c) throttling produces flash gas; (d) evaporator superheat (5-10 K) to avoid compressor liquid; (e) condenser subcooling (3-8 K). EER (BTU/Wh) and SEER (US) and SCOP (EU) are commercial KPIs — Daikin Altherma 3 H HT reaches SCOP 4.0+.

4. Worked numerical examples

Example 1 — Domestic refrigerator R-600a. T_L = -18°C (255 K), T_H = 40°C (313 K). h_1 = 528 kJ/kg, h_2 = 580 kJ/kg, h_3 = h_4 = 250 kJ/kg. COP_R = 5.35 ideal. Real 1.5-2.5 for inefficiencies. 200 W refrigerator consumes ~1 kWh/day.

Example 2 — Residential split AC R-32 (Daikin). T_L = 7°C (280 K), T_H = 35°C (308 K). h_1 = 515 kJ/kg, h_2 = 550 kJ/kg, h_3 = h_4 = 260 kJ/kg. COP_R = 7.3 ideal, 4.2 real (SEER 21). Daikin Altherma 3 H HT 8 kW R-32: SCOP 4.0.

Example 3 — Geothermal heat pump R-410A (CIAT). T_L = 5°C ground (278 K), T_H = 35°C (308 K). COP_HP = 8.3 ideal, 5.5 real. CIAT Aquaciat ILDH 60: 60 kW thermal, COP 4.8, SCOP 5.2 (Eurovent A++ class).

5. Practical applications of refrigeration cycle

• Residential AC: 1.6 billion units installed, IEA forecasts 5.6 billion by 2050. Daikin Japan global leader (29 GW installed capacity 2023), followed by Gree, Midea (China), Carrier, Trane (USA)
• Domestic refrigerators: Bosch, Whirlpool, Liebherr, LG, Samsung. R-600a propane dominant (GWP 3, A3)
• Food cold chain: industrial cold storage with NH₃ (R-717), refrigerated trucks Carrier Transicold with R-452A. Global market USD 280 billion/year
• Residential heat pumps: Daikin Altherma, Mitsubishi Ecodan, Vaillant aroTHERM, Viessmann Vitocal. Massive EU push for Green Deal: 30 million heat pumps by 2030
• Commercial refrigeration: supermarket display cases, walk-in coolers, ice machines (Manitowoc, Hoshizaki)
• Automotive refrigeration: R-134a → R-1234yf transition (GWP <1) for post-2017 EU vehicles
• Industrial high-T heat pumps: Mayekawa Heatpac (130°C), for food, chemical, paper industrial processes
• Transcritical CO₂ refrigeration: Aldi, Lidl supermarkets in EU. Carel Industries, Danfoss controls leaders

6. Comparison with other refrigeration cycles

The vapor-compression cycle dominates 99% of the market thanks to high COP, low cost, scalability from W to MW. Absorption cycle (LiBr-H₂O or NH₃-H₂O): no compressor, uses heat (solar thermal, industrial waste) — COP 0.7-1.2 but uses free energy (Yazaki, BROAD, Robur Italy). Reverse Stirling cycle (Sunpower CryoTel): for aerospace 4-150 K cryocoolers, COP 0.1-0.3. Reverse Brayton cycle (turbo-refrigeration): aerospace and LNG. Magnetocaloric refrigeration (Cooltech, Camfridge): no chemical refrigerant, uses Gd-Si-Ge magnetocaloric effect — experimental, COP 5-7, lead time 2030. Peltier thermoelectric cycle: small, no fluids, COP 0.3-0.8 for niche applications. For industrial plants, NH₃ (R-717) vapor compression remains the cost-efficiency benchmark.

7. Future developments and standards

The EU F-Gas Regulation 2024/573 mandates massive HFC phase-down: -55% by 2030 (CO₂eq), -98% by 2050. Daikin, Mitsubishi, Vaillant release R-290 (propane, GWP 3) models for air-water heat pumps. R-744 (CO₂) transcritical dominates for high-T industrial heat pumps (Mayekawa Heatpac 130°C) and EU discount supermarkets (Aldi, Lidl). HFO R-1234yf (GWP <1) replaces R-134a in automotive. Natural refrigerants (NH₃, CO₂, propane, isobutane) return after 80 years of Freon. Magnetocaloric (Cooltech Applications, Camfridge): COP 5-7, no refrigerant, lead time 2030. Water as refrigerant (R-718): Vahterus large industrial plants. High-T heat pumps Mayekawa, Star Refrigeration, Combitherm for 100-150°C industry. ASHRAE 15, EN 378 standards for safety, Ecodesign 2024/1182 and ErP EU for minimum efficiency.

Updated July 2026