How can a heat pump deliver more heat than the electricity it uses?

An electric space heater turns each kilowatt of electricity into one kilowatt of heat. A heat pump running on that same kilowatt can deliver several. That sounds like something for nothing, but no energy is created. A heat pump moves most of its heat in from outside.

Where does the extra heat come from?

On its own, heat flows downhill, from warm things to cold ones. A heat pump pushes it uphill, from cold outdoor air into a warm house. Your fridge does the same job, moving heat out of the food and into the kitchen. U.S. Department of Energy: Pump Up Your Savings with Heat Pumps.

Even freezing air holds some heat. Outside, a fluid in the heat pump's coil is made colder than the air, so heat flows into it. A compressor squeezes the fluid until it is hotter than the house. Indoors, the heat flows out into the rooms. The fluid then expands, cools and heads back outside.

The electricity runs the compressor. It pays for the climb, and it ends up as heat indoors too. So the heat delivered equals the heat collected outside plus the electrical work. OpenStax: Refrigerators and Heat Pumps.

Engineers score this with the coefficient of performance, or COP. It is the heat delivered divided by the electricity used. A space heater scores 1. Real air-source heat pumps score about 2 to 5 in mild weather. Wikipedia: Heat pump.

▶ Play with this now in Heat Pump: drag the outdoor air to −15 °C and watch the delivered heat shrink.

Why does cold weather cost more?

The bigger the climb, the more work each unit of heat costs. In our model, the house gets its heat at 45 °C (113 °F). On a 10 °C (50 °F) day, that is a climb of 35 degrees Celsius. One kilowatt of electricity delivers 4.55 kilowatts of heat.

Now drop the outdoor air to freezing, 0 °C. The climb grows to 45 degrees, and the same kilowatt delivers 3.54 kilowatts. The COP is 3.54. At −15 °C (5 °F), the climb is 60 degrees and the COP falls to 2.65.

The top of the climb matters too. On that −15 °C day, delivering heat at 55 °C gives a COP of 2.34. Delivering it at 35 °C raises the COP to 3.08. A cooler delivery temperature shrinks the climb.

Doubling the electricity doubles every flow of heat. It does not change the ratio. Only the climb does.

What does the model leave out?

Our film and the Heat Pump interactive use an illustrative energy-balance model. Their numbers are model output. They are not the performance curve of any appliance or installation.

Physics sets a ceiling for any heat pump, called the Carnot limit. It depends only on the two temperatures. For a 45-degree climb to 45 °C, the ceiling is a COP of about 7.07. Our model assumes a heat pump reaches half of it. That half is a teaching choice, not a measurement. OpenStax: The Carnot Cycle.

The model also leaves out:

• Defrosting. On cold, damp days, ice can build up on the outdoor coil and has to be melted off.
• Extra machinery. Fans, pumps and the way real units cycle on and off.
• Coil temperatures. The gap between the air temperature and the fluid's temperature inside each coil.
• Capacity. How much heat a unit can deliver in total.

At small climbs, the model allows a COP above 10. Real units fall well short of that. The trend is the point: the steeper the climb, the costlier the heat.

Can you feel a heat pump at home?

You probably own one already. A fridge is a heat pump that moves heat out of your food and into your kitchen. These steps are a suggestion, so adapt them to the child beside you.

Predict. Ask your child: the inside of the fridge is cold, so is the outside cold too? Will it feel warmer or cooler than a cupboard nearby?

Try. Wait until you hear the fridge humming, which usually means its compressor is running. Lay a hand flat on the fridge's sides, then on a nearby cupboard. Depending on the model, the warm part may be the sides, the back or a vent near the floor. Feel the vent's air with an open hand. Never reach into a vent or behind the fridge, where the fan and coils sit.

Explain. That warmth is heat taken out of your food, plus the electricity the compressor used. It is the same energy balance as a home heat pump. It also means an open fridge door cannot cool a kitchen. The fridge puts the heat it removes back into the same room, plus a little more. OpenStax: Refrigerators and Heat Pumps.

OpenStax describes a heat pump as an engine running in reverse. For the next question, explore Bartosz Ciechanowski's Internal Combustion Engine and follow heat the other way, into motion.

Heat Pump: Moving Heat Uphill is an ExplainerTools Original.