Refrigeration

Refrigerators and heat pumps move heat from cold to hot using work. Learn COP, the Carnot limit, the vapour-compression cycle (evaporator, compressor, condenser, expansion valve), refrigerants and capacity in tons.

Heat naturally flows from hot to cold. A refrigerator reverses that — pulling heat out of a cold space and dumping it into a warm kitchen — by spending work. Air conditioners, freezers, cold stores and heat pumps all use the same cycle.

Performance is measured by the coefficient of performance (COP), which is usually greater than 1: a heat pump can deliver 3–4 kW of heat per kW of electricity.

An analogy

A pump lifting water uphill: water (heat) naturally runs downhill (hot → cold), but a pump (compressor) can lift it back up, at the cost of energy.

The vapour-compression cycle

1→2 compressor raises refrigerant pressure and temperature; 2→3 condenser rejects heat to the room/outside, turning vapour to liquid; 3→4 expansion valve drops pressure (and temperature) by throttling; 4→1 evaporator absorbs heat from the cold space, boiling the refrigerant.

COP and the Carnot limit

COP falls as the temperature lift grows. A freezer (−25 °C inside, 35 °C condensing) has a much lower COP than an AC unit (5 °C evaporating, 40 °C condensing). Keeping condenser coils clean and evaporators unfrosted matters.

Refrigerants

Chosen for boiling point, pressure, capacity, safety and environmental impact. CFCs were banned for ozone depletion; HFCs (R-134a, R-410A) are being phased down for high GWP. Modern choices: R-32, R-1234yf (cars), R-290 propane, R-744 CO₂, R-717 ammonia (industrial).

Real cycles and alternatives

Real cycles include superheat, subcooling, compressor inefficiency and pressure drops. Multi-stage and cascade systems handle large lifts; transcritical CO₂ cycles work above the critical point. Absorption chillers use heat instead of work (ammonia–water, LiBr–water) — useful with waste heat.

Formulas

• Refrigerator COP: COP_R = Q_L / W
• Heat pump COP: COP_HP = Q_H / W = COP_R + 1
• Carnot limits: COP_R = T_L/(T_H − T_L), COP_HP = T_H/(T_H − T_L)
• Vapour-compression (p–h values): q_L = h₁ − h₄, w = h₂ − h₁, h₄ = h₃

Worked example: Domestic fridge

Given: Removes 300 W from the food compartment; COP_R = 2.5

Find: Power input and heat rejected.

• W = 300/2.5 = 120 W
• Q_H = 300 + 120 = 420 W

Answer: 120 W in, 420 W out to the kitchen

Worked example: Carnot limits

Given: T_L = −5 °C (268.15 K); T_H = 35 °C (308.15 K)

Find: Ideal COPs.

• COP_R = 268.15/40 = 6.70
• COP_HP = 308.15/40 = 7.70

Answer: 6.7 (fridge), 7.7 (heat pump)

Common mistakes

• Wrong: Thinking COP > 1 violates energy conservation. — Right: The fridge moves heat; it doesn't create it. Q_H = Q_L + W.
• Wrong: Using °C in Carnot COP. — Right: Temperature difference is the same in K or °C, but the numerator must be kelvin.

Applications

• Air conditioning: Split units, VRF systems and chillers — rated by EER/SEER and capacity in kW or TR.
• Heat pumps: Air- and ground-source heat pumps deliver 3–5× the electricity input as heat.
• Cold chain: Food and vaccine storage, blast freezers, supermarket CO₂ racks.

Key takeaways

• Fridges and heat pumps move heat using work.
• COP_R = Q_L/W; COP_HP = COP_R + 1.
• Evaporate → compress → condense → expand.
• Smaller temperature lift = higher COP.

Going further

• Inverter compressors: Variable-speed compressors match load, cutting cycling losses and raising seasonal efficiency (SEER) by 20–40 %.
• Transcritical CO₂: CO₂'s low critical temperature (31 °C) means heat rejection happens in a gas cooler; ejectors recover expansion work.
• Magnetocaloric & thermoelectric cooling: Solid-state alternatives avoiding refrigerants; Peltier coolers are used in small devices but with low COP.