| name | refrigeration |
| description | Refrigeration cycles — vapor compression, COP, refrigerants (R-134a, R-410A, CO₂), subcooling/superheating, multistage, absorption cycle, heat pump. |
| metadata | {"priority":6,"promptSignals":{"phrases":["refrigeration","vapor compression","COP","refrigerant","cooling cycle","heat pump","R-134a","evaporator","condenser"],"minScore":4}} |
Refrigeration — Complete Skill
Vapor Compression Cycle (Ideal)
4 processes:
1-2: Isentropic compression (compressor): s₁ = s₂, P₁→P₂
2-3: Constant-pressure condensation: reject heat Q_H = h₂ - h₃
3-4: Isenthalpic expansion (throttle valve): h₃ = h₄, P₂→P₁
4-1: Constant-pressure evaporation: absorb heat Q_L = h₁ - h₄
Performance:
COP_R = Q_L/W_c = (h₁ - h₄)/(h₂ - h₁)
COP_HP = Q_H/W_c = (h₂ - h₃)/(h₂ - h₁)
COP_HP = COP_R + 1 (always)
Carnot limits:
COP_R,Carnot = T_L/(T_H - T_L) [T in Kelvin]
COP_HP,Carnot = T_H/(T_H - T_L)
Real Cycle Modifications
Superheating at Evaporator Exit
State 1 moved to superheated vapor (e.g., 5-10°C superheat)
Prevents liquid slugging in compressor
Effect: h₁ increases slightly → COP change small (often marginal benefit)
Subcooling at Condenser Exit
State 3 moved below saturation (e.g., 5-10°C subcooling)
Increases refrigerating effect: Δq_L = c_p × ΔT_subcool
COP improves by 1-3% per degree of subcooling
Compressor Isentropic Efficiency
η_c = (h₂s - h₁)/(h₂a - h₁)
h₂a = actual enthalpy after compression
W_actual = (h₂a - h₁)/η_c × ṁ
Common Refrigerants
| Refrigerant | Type | T_boil (1 atm) | GWP | Notes |
|---|
| R-134a | HFC | -26.3°C | 1430 | HVAC, auto AC, being phased out |
| R-410A | HFC blend | -51.6°C | 2090 | Residential AC, high pressure |
| R-32 | HFC | -51.7°C | 675 | Lower GWP replacement for R-410A |
| R-1234yf | HFO | -29°C | <1 | Auto AC, replaces R-134a |
| R-717 (NH₃) | Natural | -33.3°C | 0 | Industrial, high COP, toxic |
| R-744 (CO₂) | Natural | -78.5°C | 1 | Transcritical cycle, food retail |
| R-290 (propane) | HC | -42.1°C | 3 | Flammable, domestic use |
GWP = Global Warming Potential (100-year) relative to CO₂
Phase-out: HFCs phased out per Kigali Amendment to Montreal Protocol
R-410A phase-down by 2024-2036 in US; R-32 and HFO blends replacing
Transcritical CO₂ Cycle
CO₂ T_critical = 31.1°C — above ambient → cannot condense in summer
High-side becomes supercritical (gas cooler, not condenser)
Gas cooler exit: P > P_critical, T > T_critical
Expansion through expander or throttle → mixed phase in evaporator
COP lower than HFC at high ambient temperature
Requires gas cooler pressure optimization: optimal P = f(T_amb)
Used in: food retail (supermarket), heat pump water heaters
Multistage Refrigeration
Two-stage with flash intercooler:
Flash tank (economizer) at intermediate pressure P_int
Optimal P_int = √(P_L × P_H) [geometric mean]
Advantages: lower discharge temperature, improved COP (5-15% vs. single stage)
Used when: pressure ratio > 6:1 (deep freeze: -40°C to +35°C)
Cascade system:
Two separate loops with different refrigerants
Lower cycle: R-744 or R-23 (ultra-low temp)
Upper cycle: R-134a or R-717
Heat exchanger connects them
Used for: -60°C to -100°C applications (pharmaceuticals, LNG)
Absorption Refrigeration
No compressor — uses heat instead of work
Working fluids: water (refrigerant) + LiBr (absorbent); or NH₃ + water
COP_absorption = Q_L/Q_H (heat input, not work)
COP_ideal,abs = T_L(T_H - T_0)/(T_H(T_0 - T_L)) where T_0 = ambient temperature
Actual COP_abs ≈ 0.6-0.8 (LiBr-H₂O, single effect)
Double-effect: COP ≈ 1.0-1.2
Used when: waste heat or solar available; no electricity preferred
Heat Pump Analysis
Same cycle as refrigeration but used for heating
Heating capacity: Q_H = W_c × COP_HP
Heating COP: COP_HP = T_H/(T_H-T_L) [Carnot limit]
Typical COP_HP = 2.5-4.5 (air-source), 3.5-6 (ground-source)
Air-source HP loses COP as outdoor temperature drops:
At 0°C: COP ≈ 2.5-3.5; At -20°C: COP ≈ 1.5-2.0
Balance point: outdoor T below which HP cannot meet heating demand → backup heating required
System Sizing
Refrigerating capacity Q_L:
Q_L = ṁ × (h₁ - h₄) [from enthalpy diagram]
Or: Q_L = UA × LMTD [from heat exchanger analysis]
Mass flow rate: ṁ = Q_L / (h₁ - h₄)
Compressor power: W_c = ṁ × (h₂ - h₁)
Condenser load: Q_H = ṁ × (h₂ - h₃) = Q_L + W_c
Tons of refrigeration: 1 ton = 3.517 kW = 12,000 BTU/hr (heat to melt 1 ton ice in 24 hr)
Output
Provide: COP, Q_L [kW or tons], W_c [kW], ṁ [kg/s], condenser load Q_H [kW], recommended refrigerant, superheat/subcool temperatures.
