What if a house had no insulation?

On a cold day, it is warm inside your home. A heater makes the warmth.

But warmth slowly sneaks out through the walls. What if nothing slowed it down?

Warmth always moves from warmer places to cooler ones. On a winter day, that means heat is always escaping from your home through the walls, roof, windows and floor. The heater's job is to replace it.

Many homes have insulation: material hidden in the walls and roof that slows the heat down. In this lab, the outside temperature is 0 °C, freezing point. What happens to the house, and to its heater, if you take the insulation away?

Heat flows down a temperature gradient: from the warm interior through the building envelope to the cold air outside. The rate depends on the temperature difference, the envelope's area and how readily its layers conduct heat, summarized as a U-value.

This lab models a house with a 300 m² outer shell, a thermostat set to 20 °C and a 10 kW heater, on a day that stays at 0 °C. It compares an insulated shell (U = 0.6 W/m²·K) with an uninsulated one (U = 2 W/m²·K).

Our house has insulation in its walls and roof. It is like a warm coat.

The heater turns on, then off, then on again. The house stays cozy all day.

In the insulated house, heat leaks out at about 3.6 kilowatts, all day and all night. The 10-kilowatt heater easily keeps up. It switches on and off to hold 20 °C, running only about a third of the time.

Over a whole day, it puts in about 86 kilowatt-hours of heat. The thermostat clicks on when the house dips just below 20 °C and off again just above it.

With U = 0.6 W/m²·K, the loss at 20 K is 0.6 × 300 × 20 = 3,600 W. The heater, at 10 kW, runs 36% of the time, delivering 86.4 kWh per day; over the model's 48-hour run it uses about 172 kWh.

The house's heat store of 25 MJ/K gives a cool-down time constant C ÷ (U·A) of 38.6 hours: if the heating failed, the gap between inside and outside would shrink slowly.

Now Olly takes the insulation out. Warmth rushes out through the walls much faster.

The heater stays on all the time. But the house still gets cooler!

Remove the insulation and the heat loss would jump to about 12 kilowatts at 20 °C, more than three times as much. The 10-kilowatt heater can't keep up. It runs nonstop, and the house slowly cools until it settles at about 17 °C, where the leak finally matches the heater.

A bigger heater could hold 20 °C, but it would need about 288 kilowatt-hours of heat a day, more than three times the insulated house.

With U = 2, the loss at 20 K would be 12 kW. The heater's 10 kW balances the loss only when ΔT = 10,000 ÷ 600 = 16.7 K, so the house settles at 16.7 °C with the heater on 100% of the time: 240 kWh a day. In the 48-hour run it falls to 18.5 °C after 6 hours, 17.1 °C after 24 and 16.7 °C by the end.

Give it a 15 kW heater and it holds 20 °C, but needs 288 kWh a day, 3.33 times the insulated house, exactly the ratio of the U-values. The time constant shrinks to 11.6 hours.

Insulation is a layer inside the walls and roof. Heat has a hard time getting through it.

Without it, the warmth slips out through the walls fast. The heater has to work much harder.

Heat leaks through a wall faster when the wall lets heat through easily, when the wall is bigger and when it is colder outside. Insulation slows the leak. Insulation is rated with a number called the R-value: the higher the number, the better it resists heat.

Our model is simple. It gives the whole house one leakiness number and one temperature. It leaves out drafts through gaps, which in real houses can let out a lot of heat, and it ignores sunshine and the warmth from people and appliances.

Conductive loss is Q = U·A·ΔT, where U falls as the envelope's resistance to heat flow (its R-value) rises. Insulation adds resistance, cutting U. Steady energy use scales linearly with U, while a fixed-size heater sets a ceiling on the indoor temperature: T_out + P ÷ (U·A).

Model limits: one average U for walls, roof, windows and floor together, no air leakage or ventilation, no solar or internal gains, one uniform temperature and a constant outdoor temperature. The values are typical, not measurements of a real house.

Real homes use lots of energy to stay warm or cool.

People add insulation and fill in drafty gaps. That keeps the warmth in and saves energy.

Keeping homes warm and cool takes a lot of energy. The U.S. Energy Information Administration found that in 2020, heating and air conditioning together used more than half of an average American household's energy.

ENERGY STAR says that sealing air leaks and adding insulation can save up to about 10 percent on a home's yearly energy bills. University of Illinois Extension experts suggest finding and sealing air leaks around doors, windows and attic hatches before adding insulation. They also say sealing wall leaks and drafts can cut up to a fifth of a winter energy bill.

The U.S. Energy Information Administration reports that in 2020, 52% of an average household's annual energy use went to space heating and air conditioning, and that apartments use a smaller share, partly because neighboring units shield them from the weather. ENERGY STAR estimates that sealing air leaks and adding insulation can save up to 10% on annual energy bills.

University of Illinois Extension describes the R-value as a measure of how well insulation resists heat flow and advises sealing air leaks before adding insulation. That matches this model's main omission: real heat loss includes air leakage as well as conduction.