Carnot Efficiency & Refrigeration COP
Maximum theoretical efficiency for a power cycle (Carnot) and coefficient of performance for refrigeration and heat pump cycles. Compares to typical real-world equipment efficiencies. Energy implications of temperature-lift changes.
Defaults: refrigeration 90°F condenser to 40°F evaporator (50°F lift), 55% of Carnot — typical commercial chiller. Cooling 1000 ft² office in DFW summer requires ~3 tons.
Carnot — the upper bound, never reached
Carnot efficiency / COP is the theoretical maximum from thermodynamics — no real device can exceed it. Real equipment achieves 40–70% of Carnot:
- Steam turbine cycle: η_real ≈ 0.35; Carnot at 540°C → 25°C ≈ 0.63 → ratio = 0.55
- Combined cycle gas turbine: η_real ≈ 0.55–0.62; Carnot at 1300°C → 25°C ≈ 0.81 → ratio ≈ 0.7
- Centrifugal chiller: COP_real ≈ 5–7; Carnot at 95°F → 42°F ≈ 9.5 → ratio ≈ 0.55
- Air-source heat pump: COP_real ≈ 3–4 in mild weather; ratio ≈ 0.45–0.55
- Geothermal heat pump: COP_real ≈ 4–5; ratio ≈ 0.55–0.65 (steady ground T helps)
Lift sensitivity
Refrigeration COP is dominated by the temperature lift (T_H − T_C). Cutting lift by 10°F can boost COP by 30%. Designers minimize lift by:
- Higher chilled water: 44°F instead of 42°F → 7% better COP
- Lower condenser water: 80°F instead of 90°F → 25% better COP
- Free cooling / waterside economizer: when outside wet-bulb < 50°F, bypass the chiller entirely
- Variable-speed condenser fans: reduce condenser approach in cool weather
- Larger heat exchangers: lower approach temperatures = lower lift
EER, SEER, IEER
- EER (Energy Efficiency Ratio, US units): Btu/(W·hr) — instantaneous, at AHRI rating point. Equals 3.412 × COP.
- SEER (Seasonal): weighted average over a typical cooling season at varying outdoor conditions.
- IEER (Integrated, commercial): weighted at 4 part-load conditions for commercial chillers.
- kW/ton: HVAC industry preference. Lower is better. 1 kW/ton ≈ 3.516 EER.
2030 minimum efficiency standards: chiller IEER ≥ 0.7 kW/ton (≈ 5 COP), residential AC SEER ≥ 14 (5+ region 1).
Heat pump = refrigeration in reverse
The same vapor-compression cycle can pump heat in either direction:
- Refrigeration: Q_C is the useful effect (cooling). COP = Q_C / W.
- Heat pump: Q_H is the useful effect (heating). COP = Q_H / W = COP_ref + 1.
A heat pump always delivers more heating than the electricity it consumes (COP > 1) — it's "leveraging" outside heat. At 35°F outdoor, COP ≈ 3 means 3 units of heat for 1 unit of power. Compare to electric resistance: COP = 1.0 always.
Why temperatures must be absolute
Carnot's derivation uses absolute temperature ratios. Using °C or °F gives wrong results — sometimes negative or undefined. Always convert: K = °C + 273.15, °R = °F + 459.67.
Reference: Cengel, Y.A., Boles, M.A. (2015). Thermodynamics: An Engineering Approach, 8th ed., McGraw-Hill, ch. 6 & 11. ASHRAE Handbook Refrigeration (2022).