Mass stores heat and insulation keeps it, and how long a store lasts is set by its time constant, the heat capacity divided by the rate of heat loss per kelvin. Two tonnes of brick holds 1.68 MJ per kelvin, so over a heat loss of 50 W/K the time constant is 9.3 hours, and doubling the heat loss halves it to 4.7 hours. Put the mass inside the insulation and make the insulation as good as the store is large.
Part of Thermal Mass Fundamentals
Insulation and thermal mass are partners: mass stores the heat, insulation slows its escape, and neither works alone.
The Time Constant
A store at a temperature above its surroundings loses heat at a rate UA × ΔT, where UA is the loss per kelvin (watts per kelvin) and ΔT is the temperature difference. Its heat capacity is C joules per kelvin. The temperature difference then decays exponentially with time constant τ = C ÷ UA: after one τ, 37% of the original difference remains (e^-1 = 0.37); after 2τ, 14%.
Inputs, assumed: 2,000 kg of brick inside a small cabin, c = 0.84 kJ/kg·K (parent page) so C = 2,000 × 0.84 = 1,680 kJ/K = 1.68 MJ/K; envelope loss UA = 50 W/K (assumed).
- τ = 1,680,000 J/K ÷ 50 W/K = 33,600 s = 9.3 hours.
- With UA doubled to 100 W/K, τ = 16,800 s = 4.7 hours.
- After 12 hours at τ = 9.3 h, the temperature difference above outside has fallen to e^(−12 ÷ 9.3) = 0.275, so if mass and room started 20 K above the outside air, they stand at 5.5 K above it.
So insulation multiplies the useful life of a given mass: halve the heat loss and double the time. And the reverse is the problem of an uninsulated mass: it matters little how much stone you pile up if the room loses heat at 100 W/K.
Place The Mass Inside
A massive wall outside the insulation stores heat where it is lost to the weather; inside the insulation it returns it to the room. The wiki’s house pages work an example: 6 m³ of stone outside the envelope soaks up heat, then gives it to the air outdoors (Where to Insulate vs Where to Mass). Insulation on the outside of mass also lets the mass stay near the room temperature (Insulation Strategies).
Mass has a second job: it smooths the daily swing. How deep it needs to be is a separate question; roughly the outer 10-15 cm of a thick wall does the daily work (Heat Absorption & Release Cycles).
What You Need
- An estimate of heat loss in watts per kelvin: measure how fast the room cools overnight
- The mass in kilograms and its specific heat
- Dry insulation (Insulation Materials Ranked)
- A thermometer
Method: Measure Your Own Time Constant
Step 1: Warm the room and mass with a fire, then let it cool without further heat.
Step 2: Read the room and outdoor temperature every two hours.
Step 3: Find the time for the difference to fall to 37% of its starting value. That is τ.
Step 4: Improve insulation until τ is long enough to carry you through the night.
Common Mistakes
- Mass without insulation.
- Insulation without mass. The room swings quickly between warm and cold.
- Mass in the shade. It never charges.
Safety
A heavily insulated hot mass stays dangerous longer
Better insulation means a hot surface stays hot for longer: a store at 60°C or above burns in seconds on contact and remains hot after the fire is out. Keep children and the elderly, who burn at lower temperatures and shorter exposures than adults, away from hot surfaces, and keep combustibles clear of the insulation around a hot mass.
What’s Next
- Learn next: Rock & Sand Heat Stores — using mass at a larger scale
- Combine with: Super-Insulation — insulating a water store