Refrigeration and Heat Pumps
The vapor-compression cycle, COP, the Carnot limit, refrigerant tables, and sizing a compressor with a worked R-134a example.
The vapor-compression cycle
Refrigeration moves heat from a cold space to a warmer one, which the second law (see The Second Law, Entropy and Carnot) says needs work. The vapor-compression cycle does this with a fluid that evaporates at low temperature and condenses at a higher one, by changing its pressure:
- 1 → 2 Compressor: low-pressure vapor is compressed, raising its pressure and temperature.
- 2 → 3 Condenser: the hot vapor rejects heat qH to the surroundings and condenses to liquid.
- 3 → 4 Expansion valve: the liquid is throttled to low pressure; some flashes to vapor and the mixture becomes cold. Enthalpy is constant, h₄ = h₃.
- 4 → 1 Evaporator: the cold mixture absorbs heat qL from the space and evaporates.
COPcooling = qL ÷ w = (h₁ − h₄) ÷ (h₂ − h₁) COPheating = qH ÷ w = (h₂ − h₃) ÷ (h₂ − h₁)
Worked example: R-134a
Worked example: a 3.5 kW freezer
Refrigerant R-134a evaporates at 0.14 MPa (−18.8 °C) and condenses at 0.8 MPa (31.3 °C). From the refrigerant tables: h₁ = 239.16 kJ/kg (saturated vapor), h₂ = 275.39 (compressed isentropically) and h₃ = 95.47 (saturated liquid). The valve keeps h₄ = h₃.
- Refrigeration effect qL = 239.16 − 95.47 = 143.69 kJ/kg.
- Compressor work w = 275.39 − 239.16 = 36.23 kJ/kg; heat rejected qH = 179.92 kJ/kg.
- COP = 143.69 ÷ 36.23 = 3.97. As a heat pump the same cycle gives 4.97.
- For a 3.5 kW load the refrigerant flow is ṁ = 3.5 ÷ 143.69 = 0.0244 kg/s (88 kg/h). The compressor power is 0.0244 × 36.23 = 0.882 kW and the condenser rejects 4.38 kW. The load is 1.00 tons of refrigeration (1 ton = 3.517 kW).
- Compressor displacement: the suction vapor has v₁ = 0.14649 m³/kg, so it must pump 12.8 m³/h at the inlet: the large volume of low-pressure vapor is why refrigeration compressors are big.
COP and the Carnot limit
The best possible COP between two temperatures is the Carnot value, COPcooling = TL ÷ (TH − TL) and COPheating = TH ÷ (TH − TL). It falls rapidly as the temperature lift grows.
For the freezer above, TL = 254.4 K and TH = 304.5 K, so the Carnot COP is 5.08. The ideal cycle’s 3.97 is 78 percent of Carnot; a real compressor, motor and heat exchangers bring it down to roughly 50 to 65 percent of Carnot, about 3.0. Seasonal ratings (SEER, SCOP) are worked out the same way over a year of weather.
Heat pumps
A heat pump is a refrigerator that cares about the hot side: it heats a building by lifting heat from the air, ground or water. Because the output is more than the electrical input, it beats resistance heating by a wide margin.
Worked example: heating a house
- The house needs 8 kW. An air-source heat pump lifts heat from 5 °C air to 35 °C floor-heating water: Carnot COP = 308.15 ÷ 30 = 10.3; a real machine at half of Carnot gives COP ≈ 5.1.
- Electrical input = 8 ÷ 5.1 = 1.56 kW, compared with 8 kW for resistance heaters: a saving of 81 percent.
- Over a 1 500 hour season at 0.15 per kWh: heat pump 350, resistance 1 800.
- Raise the water to 55 °C for radiators and the Carnot COP drops: the real COP is 3.3. Low-temperature emitters (underfloor or oversized radiators) matter.
Components and refrigerants
| Part | Job | Notes |
|---|---|---|
| Compressor | raise the pressure of the vapor | reciprocating, scroll, screw, centrifugal; hermetic in small units; only vapor must enter (liquid slugging destroys it) |
| Condenser | reject heat and condense | air-cooled or water-cooled; subcool the liquid a few kelvin |
| Expansion device | drop the pressure | capillary tube, thermostatic or electronic expansion valve; controls superheat |
| Evaporator | absorb heat and evaporate | superheat the vapor 5 to 10 K before the compressor |
| Refrigerant | carry the heat | R-134a, R-410A, R-32, R-290 (propane), R-744 (CO₂), R-717 (ammonia); choose by pressure, safety class, global warming potential |
Refrigerant regulations are tightening: high-GWP gases (R-134a, R-410A) are being phased down in favor of R-32, R-290 and CO₂. Flammable and toxic refrigerants need design to the safety standards, and refrigerant work needs certification in many countries.
Real systems and improvements
- Superheat and subcooling improve the cycle and protect the compressor.
- Two-stage compression with flash-gas removal helps for low evaporator temperatures.
- Compressor isentropic and volumetric efficiency (60 to 85 percent) sets the real work.
- Defrost cycles cost energy at low evaporator temperatures; an air-source heat pump loses COP below about 0 °C.
- Absorption chillers use heat instead of electricity (lithium bromide–water or ammonia–water), with COP of 0.7 to 1.2: useful where waste heat is free.
Related
- Previous: Gas Cycles: Otto, Diesel and Brayton. Next: Combustion and Boiler Efficiency.
- Heat Transfer for evaporator and condenser design.
- Psychrometric Calculator for cooling and dehumidification.
- Thermodynamics and Steam: the whole guide.
FAQ
Why can a COP be greater than 1?
A refrigerator or heat pump moves existing heat rather than generating it, so the heat delivered is the work plus the heat taken in.
What is superheat in a refrigeration system?
The temperature of the vapor above its saturation temperature as it leaves the evaporator. A few kelvin ensures only vapor reaches the compressor.
Why do heat pumps struggle on cold days?
The lift between outside air and the supply water is larger, so the COP falls, and the heat demand is highest.
What is a ton of refrigeration?
12 000 BTU/h, or 3.517 kW: the cooling of melting one US ton of ice in 24 hours.
References
- Çengel, Y. A. and Boles, M. A., Thermodynamics: An Engineering Approach, McGraw-Hill (refrigeration cycles, R-134a tables).
- ASHRAE Handbook – Refrigeration and Fundamentals; ASHRAE Standard 34 (refrigerant safety classes).
- Stoecker, W. F., Industrial Refrigeration Handbook, McGraw-Hill.
Last reviewed: October 2026. Table values are from the R-134a tables; real COPs are typical.