12.2 Refrigeration cycles

Refrigeration Cycles

Purpose of Refrigeration Cycles

A refrigeration cycle moves heat from a cold space to a warmer environment. This goes against the natural direction of heat flow, so it requires external work input to make it happen.

The Second Law of Thermodynamics tells you that heat spontaneously flows from hot to cold. A refrigeration cycle reverses this natural flow by using a circulating refrigerant in a closed loop. The refrigerant exploits phase changes to do the heavy lifting: it absorbs heat when it evaporates inside the cold space, then releases that heat when it condenses in the warmer environment.

Components of the Vapor-Compression Cycle

The vapor-compression cycle is the most widely used refrigeration system. It has four main components, and the refrigerant passes through each one in sequence:

1. Evaporator — A heat exchanger where the low-pressure, low-temperature refrigerant absorbs heat from the cold space and evaporates into a vapor. This is where the actual cooling happens.
2. Compressor — Takes the low-pressure vapor from the evaporator and compresses it to high pressure and high temperature. This is the component that consumes external work (usually electrical energy).
3. Condenser — A heat exchanger where the high-pressure, high-temperature vapor releases heat to the ambient environment and condenses back into a liquid. The heat rejected here equals the heat absorbed in the evaporator plus the work added by the compressor.
4. Expansion valve (also called a throttling valve) — Drops the pressure and temperature of the liquid refrigerant rapidly before it re-enters the evaporator. No work is done here; the pressure drop occurs through a restriction in the flow path.

The cycle then repeats: low-pressure liquid enters the evaporator, absorbs heat, and the loop continues.

Performance Analysis of Refrigeration

The coefficient of performance (COP) measures how effectively a refrigeration cycle uses work input to remove heat. It's defined as:

$COP_R = \frac{Q_L}{W_{in}}$

where $Q_L$ is the heat removed from the cold space and $W_{in}$ is the work input to the compressor. Notice that COP can be greater than 1, which sometimes surprises students. This doesn't violate any law; it just means you're moving more energy as heat than you're spending as work.

Since energy is conserved around the cycle, the heat rejected at the condenser equals the sum of the two inputs:

$Q_H = Q_L + W_{in}$

You can rearrange this to express COP in terms of the heat quantities alone:

$COP_R = \frac{Q_L}{Q_H - Q_L}$

Factors that affect COP:

1. Temperature difference between the cold space and the ambient environment. A smaller temperature difference means less work is needed, so COP increases. This is why your refrigerator works harder (lower COP) on a hot day.
2. Compressor efficiency. A more efficient compressor wastes less energy on friction and irreversibilities, so more of the work input goes toward moving heat.
3. Refrigerant properties. A refrigerant with a higher latent heat of vaporization can absorb more heat per unit mass in the evaporator, which tends to improve COP. Lower liquid specific heat capacity also helps, because less of the cooling effect is lost during the expansion process.

For an ideal (Carnot) refrigeration cycle operating between a cold reservoir at $T_L$ and a hot reservoir at $T_H$ (both in Kelvin), the maximum possible COP is:

$COP_{Carnot} = \frac{T_L}{T_H - T_L}$

Real cycles always fall below this theoretical limit due to irreversibilities like friction, pressure drops, and heat transfer across finite temperature differences.

Environmental Impact of Refrigerants

Early refrigerants like chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) were effective but caused serious ozone depletion and contributed to global warming. The Montreal Protocol (1987) established a global phaseout of these substances.

Replacement options include:

• Hydrofluorocarbons (HFCs) — Zero ozone depletion potential, but they still have high global warming potential (GWP). The Kigali Amendment (2016) now targets a phasedown of HFCs as well.
• Natural refrigerants — Substances like ammonia ($NH_3$), carbon dioxide ($CO_2$), and hydrocarbons (propane, isobutane) have very low GWP. Ammonia is widely used in industrial systems. $CO_2$ is gaining popularity in commercial refrigeration. Hydrocarbons work well but are flammable, so they're typically limited to small-charge systems.

Proper handling, recovery, and recycling of all refrigerants remain critical to preventing atmospheric release and minimizing environmental harm.