Cooling a room with a fridge

Why does leaving the fridge door open in a closed room make the room warmer rather than cooler?

Stand in front of an open fridge on a hot day and the relief is immediate and real. Cold air spills out over your feet. So the obvious extension suggests itself: leave the door open, shut the kitchen door, and let the appliance work on the whole room.

It runs backwards. The sealed kitchen ends up warmer than if you had left the fridge alone — and that is strange, because the machine plainly does make cold air. Where does the arithmetic turn on us?

Let us not re-derive the refrigeration cycle; that lives in its own walk-through. Take only its conclusion: a fridge does not manufacture cold, it moves heat to the coils on its back, and it needs a compressor doing work to push heat where it would not go on its own.

Now stop looking inside the machine and draw a line around the whole room instead. Seal it: no windows, no doors, insulated walls. What crosses that line? Only one thing — the electricity in the power cable.

Ask what becomes of that electricity. It turns the compressor, spins fans whose stirring dies away as friction, lights the little bulb whose light lands on a surface and warms it. Every thread ends in the same place: energy is conserved, and inside a sealed room there is nowhere for it to go but the air, the walls, the food and the machine. The room's internal energy rises by exactly the electrical energy consumed. Not approximately — exactly.

What of the heat the fridge so visibly removes from the compartment? It was already inside our line. Taking a hundred joules out of the milk and putting them into the kitchen air moves energy from one side of the room to the other; the sum across the room is unchanged. Only the electricity is new.

So the accounting is short: heat out of the coils equals heat taken from the compartment plus the work supplied. The first term is a transfer within the room and cancels. The second does not. Leave the door open and the machine can never satisfy its thermostat, so it runs continuously — a small electric heater of a hundred watts or so, permanently on, dressed as a cooler.

Then why does it feel like it works? Because it genuinely does redistribute. There is cold air at the door and hotter air at the coils, and standing in one place while ignoring the other is exactly the mistake. That is the whole trick of every cooling device: not to destroy heat but to choose where to put it.

Which tells us what an air conditioner really is. Physically it is the same machine; the only difference that matters is where its condenser sits — outside the boundary you care about. The window unit's hot half hangs over the street; the split system's outdoor box stands in the garden. An air conditioner is a fridge that has been given somewhere else to dump its heat, and its cooling power is precisely the cooling that fridge would give you if you could hold its back coils out of the window.

Two refinements are worth making explicit.

First, there is no cleverness that rescues the plan. You might hope a very efficient fridge would tip the balance — and with the door open the temperature gap it works across nearly vanishes, so it moves heat unusually well per joule spent. It makes no difference. Efficiency governs how much heat gets shuffled, and shuffling cancels. The room's gain is the electricity, and only the electricity, for any machine at any efficiency. That is the second law showing its teeth: no device operating entirely within a closed system can lower that system's energy, because the device must dissipate its own work inside it.

Second, the same accounting explains why heat pumps are not a swindle. A heat pump warming your house in winter delivers several joules of heat per joule of electricity — because most of what it delivers was scavenged from the cold outdoors and carried in. It has an outside. Run that same machine with both its coils indoors and its advantage collapses to exactly one joule per joule, the performance of a bar heater. The multiplier was never in the machine; it was in the boundary.

• Why a portable air conditioner with two hoses beats a single-hose one, and by how much.
• How a data centre's cooling bill is really a bill for moving heat somewhere it can be rejected.

Every term the collection defines is gathered in the glossary.