Physics · Molecular physics and thermodynamics · Grade 10

Refrigerator and heat pump

How does heat flow “uphill” from a cold fridge into a warm kitchen?

The situation

In summer the kitchen temperature in Tashkent rises above 30 °C, while inside the fridge it is +4 °C. Heat always flows by itself from hot to cold — so how does heat from inside the fridge get out through the black grille at the back into the hot kitchen? In winter the same machine works in reverse, “sucking” heat from the street at −5 °C to warm the house, and uses 3–4 times less electricity than an electric heater. We will cut the refrigerator open and follow the path of the refrigerant. How much work is needed to move heat from cold to hot, and can it be reduced?

Topic

Refrigerator and heat pump. Home fridge-freezer and air conditioner: how heat moves from cold to hot

Key ideas

Refrigeration cycle
COP and the Carnot limit
Second law of thermodynamics

Formulas

Q_{1} = Q_{2} + A

Conservation of energy: the condenser gives the room the sum of the heat $Q_{2}$ taken from inside the fridge and the compressor work $A$ .

ε = \frac{Q_{2}}{A}, φ = \frac{Q_{1}}{A} = ε + 1

The coefficient of performance (COP) of cooling and the heating coefficient of a heat pump.

ε_{K} = \frac{T_{2}}{T_{1} - T_{2}}, φ_{K} = \frac{T_{1}}{T_{1} - T_{2}}

The Carnot limit: $T_{2}$ — temperature of the cold body, $T_{1}$ — of the hot body (in kelvins). A real machine is always worse.

\frac{Q_{1}}{T_{1}} \geq \frac{Q_{2}}{T_{2}}

The second law (in terms of entropy): the entropy delivered to the hot body is not less than that taken from the cold body — so $A > 0$ is necessary.

E_{m o n t h} = \overline{P} \cdot 720 h

Monthly electricity consumption: average power × 30 days. 1 kW·h = 3.6 MJ.

Theory

Refrigeration cycle

Inside the fridge circulates a substance that boils at low pressure — the refrigerant (everyday name “freon”; in this fridge it is isobutane, R600a). In the evaporator (the aluminium box at the top) it boils at a temperature 10–15 °C lower than the compartment (≈ −8 °C for a compartment at +4 °C, −20…−25 °C in the freezer) and takes heat $Q_{2}$ from the food — boiling requires latent heat. The compressor squeezes the vapour from ≈ 1 bar to 5–7 bar, and it heats up to 60–90 °C. In the condenser at the back the vapour gives heat $Q_{1}$ to the room air and turns into liquid. A thin capillary tube sharply lowers the pressure (throttling, the enthalpy does not change): the liquid partly evaporates, cools, and goes on to the evaporator again. In the scene the colour of the particles shows temperature, and their size shows liquid (large) or vapour (small).

Energy balance, COP and Carnot

The compressor's work is not lost: $Q_{1} = Q_{2} + A$ — the back of the fridge gives out even more heat than was taken from inside. The coefficient of performance $ε = Q_{2} / A$ is often greater than 1: this is not “producing” energy but moving heat. For an ideal (Carnot) machine $ε_{K} = T_{2} / (T_{1} - T_{2})$ : the smaller the temperature difference, the better. The real $ε$ is much smaller: the evaporator must be colder than the compartment and the condenser hotter than the room (so that heat can flow), and there are losses in the compressor and motor too. Compare the two Carnot values on the panel. In a hot kitchen the fridge works harder: heat leaks in faster, while $ε$ falls.

Second law of thermodynamics

Clausius' statement: heat does not pass by itself from a cold body to a hot one. Switch off the “Compressor” button: the refrigerant stops, heat leaks in from the room through the walls, and the compartment warms up to room temperature. To transfer heat in the opposite direction, external work is needed. In terms of entropy: if entropy $Q_{2} / T_{2}$ is taken from the cold body, at least as much — $Q_{1} / T_{1} \geq Q_{2} / T_{2}$ — must be given to the hot body, so $Q_{1} > Q_{2}$ and $A > 0$ . A heat engine is the reverse of this same cycle (see the engine experiment).

Heat pump and air conditioner

In a split air conditioner a four-way valve reverses the direction of the refrigerant. In summer the indoor unit is the evaporator: it takes heat from the room and releases it outdoors through the outdoor unit. In winter the outdoor unit becomes the evaporator and takes heat even from cold air (the refrigerant is colder still), while the indoor unit is the condenser and heats the room. The heating coefficient $φ = Q_{1} / A$ is usually 2.5–4: 1 kW·h of electricity gives 2.5–4 kW·h of heat. An electric heater has $φ = 1$ . The colder it is outside, the lower $φ$ becomes. Model: for the house $U A = 160$ W/K, an inverter compressor, refrigerant properties from simplified formulas (accurate to a few per cent), time sped up 60 times.

Refrigerators and the environment

Earlier fridges used chlorofluorocarbon refrigerants (R12); when it was found that, released into the atmosphere, they destroy the ozone layer, the 1987 Montreal Protocol phased them out. The next one, R134a, does not harm ozone but is a strong greenhouse gas. Today domestic fridges use isobutane (R600a), and air conditioners R410A and R32. A fridge runs continuously all year round: an efficient (class A) model and correct use — closing the door quickly, letting hot food cool first, cleaning dust from the grille at the back, not putting it next to the stove — reduce electricity use and the CO₂ that comes with it. The refrigerant in an old fridge must be recovered by a special procedure.

Very low temperatures: magnetic and nuclear cooling

A gas cycle is no use for cooling to fractions of a kelvin. Adiabatic demagnetisation: a paramagnetic salt is cooled with liquid helium in a strong magnetic field — the spins become ordered and the heat released goes into the helium. Then the salt is thermally isolated and the field removed: for the spins to become disordered they take energy from the crystal lattice, and the temperature falls to millikelvins. Doing the same with nuclear spins reaches microkelvins. Magnetocaloric refrigerators that work at room temperature (for example, based on gadolinium) are also being developed. In detail — in the magnetic properties experiment.

Did you know?

After it was found that chlorofluorocarbon refrigerants destroy the ozone layer, the Montreal Protocol was adopted in 1987. Most of today's domestic fridges use isobutane (R600a), which is harmless to ozone.
The idea of cooling a paramagnetic salt by adiabatic demagnetisation was proposed independently in 1926–1927 by Peter Debye and William Giauque; this method reaches millikelvin temperatures.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

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