Refrigeration & Heat Pumps

Running a cycle backwards

Lesson 5 showed that a Carnot engine run backwards becomes a refrigerator or heat pump: put in work, and heat moves from cold to hot. The first law is satisfied — heat delivered equals heat absorbed plus work — and the second law sets the price. The best possible coefficients of performance between a cold space at $T_C$ and a warm one at $T_H$ are

$\beta_\text{max} = \frac{T_C}{T_H - T_C}, \qquad \gamma_\text{max} = \frac{T_H}{T_H - T_C}.$

A heat pump moving heat from 0 °C outdoors to 35 °C indoors could, in principle, deliver almost 9 units of heat per unit of work. The heat isn't made; it's moved — scavenged from the cold outdoor air and lifted to a useful temperature. The electricity pays only for the lift.

The vapour-compression cycle

Real refrigerators don't use gas pistons. They exploit boiling and condensation, which absorb and release large amounts of heat at constant temperature — exactly what a Carnot cycle wants. The vapour-compression cycleVapour-compression cycleThe cycle of almost every refrigerator and heat pump: compressor, condenser, expansion valve, evaporator. has four components:

1. Evaporator (4 → 1): cold liquid–vapour refrigerant at low pressure boils, absorbing heat $\cheat{Q}_L$ from the refrigerated space.
2. Compressor (1 → 2): the vapour is compressed to a high pressure — and becomes hot. This is where the work goes in.
3. Condenser (2 → 3): the hot vapour gives up heat $\cheat{Q}_H$ to the surroundings and condenses to liquid.
4. Expansion valve (3 → 4): the liquid throttles back to the low pressure, flashing partly to vapour and cooling dramatically — Lesson 4's throttle, at constant enthalpy.

Refrigeration engineers draw it on a pressure–enthalpy chart, where all four processes are simple lines and every energy is a horizontal distance:

$\beta = \frac{\cheat{q}_L}{\cwork{w}} = \frac{h_1 - h_4}{h_2 - h_1}, \qquad \gamma = \frac{\cheat{q}_H}{\cwork{w}} = \frac{h_2 - h_3}{h_2 - h_1} = \beta + 1.$

Two things keep a real cycle below Carnot. The throttle is irreversible — a turbine expanding the liquid could recover some work, but it would be too small to be worth it. And the compressor generates entropy and delivers superheated vapour hotter than the condensing temperature. Domestic fridges reach about half the Carnot COP; large chillers rather more.

Choosing a refrigerant

The working fluid should boil at a convenient pressure at the evaporator temperature (not far below atmospheric, so air doesn't leak in), condense at a manageable pressure at the condenser temperature, carry a lot of latent heat per kilogram, and be non-toxic, non-flammable and stable. Early refrigerators used ammonia, sulphur dioxide and methyl chloride — effective but dangerous. The CFCs that replaced them in the 1930s were safe in the kitchen and catastrophic for the ozone layer; their HFC successors, like the R-134a used here, are ozone-safe but potent greenhouse gases. The industry is now moving to low-global-warming fluids: hydrocarbons such as propane and isobutane, CO₂, ammonia again for large plants, and new HFOs.

Heat pumps

A heat pump is the same machine with the opposite purpose. Its evaporator sits outdoors, absorbing heat from the air, the ground or a river; its condenser heats a house's radiators or hot water. Moran and Shapiro's point from Lesson 7 comes back with force: burning gas at 1900 K to produce heat at 40 °C destroys most of its exergy. A heat pump delivers the same heat from a fraction of the work.

Next: the tables and charts we have used are full of properties nobody can measure directly — entropy, enthalpy. Why do a handful of measurements determine everything else?