Building Temperature Drift in a Heating Outage

ScopeWhen the power or the gas goes out in a winter storm, the question for an occupant, a building manager, or a utility triaging restoration is how many hours until the building is too cold to live in, or cold enough that pipes in the outside walls are at risk. This calculator answers it with the lumped-capacitance (Newton cooling) model. The time constant is the heat the building stores per degree divided by the heat it loses per degree, tau = C / UA; the building drifts toward an equilibrium set by the outdoor temperature plus its internal gains divided by UA, fast at first and slower as it gets close. Enter the UA from the Whole-Building Heat-Loss Coefficient UA calculator and the thermal capacitance directly, or let the helper add up mass times specific heat for gypsum, wood, concrete, and water. The small house from the Whole-Building Heat-Loss Coefficient UA calculator (UA 309.7 Btu/h-degF) with 10,000 Btu/degF of capacitance, at 68 degF when the power fails and 10 degF outside, has a 32.3 h time constant: 12.0 h to 50 degF and 21.3 h to 40 degF, and 37.6 degF after a day. Four people at home (about 250 Btu/h each) raise the settling point to 13.2 degF and push 40 degF out to 23.1 h; the 17% UA cut from air sealing and better glass pushes it to 25.6 h, so the efficiency upgrade is also a resilience upgrade. It is a single-node estimate: the room air cools faster than the curve at first, exterior-wall and crawl-space pipes freeze well before the room does (the Water Pipe Freeze Time calculator), and solar gain, wind, and zoning are not modeled. The capacitance dominates and is an estimate. Never heat with a grill or generator indoors. The mechanical contractor or engineer and local emergency guidance govern.

Formula or tabletau = C / UA (h); T_eq = T_out + Q_internal / UA with about 250 Btu/h per person; T(t) = T_eq + (T_start - T_eq) x e^(-t / tau); hours to a threshold = tau x ln((T_start - T_eq) / (T_threshold - T_eq)), never reached when the threshold is at or below T_eq.

Source and editionThe lumped-capacitance (Newton cooling) model by name, with the hours-of-safety thermal-resilience metric of Lawrence Berkeley National Laboratory, Assessing thermal resilience of an assisted living facility during heat waves and cold snaps with power outages (OSTI 1984644), and material specific heats per ASHRAE Handbook -- Fundamentals by chapter. The UA comes from building-ua; the capacitance is entered or built from masses.

Free accessThe LBNL report is free at osti.gov (OSTI 1984644); the method is a textbook first-order decay on the user's own UA and capacitance, and no ASHRAE table is reproduced -- four round specific heats are physical data.

What governsEstimate. AHJ and licensed mechanical contractor govern. ACCA Manual J / D / S supersede rules of thumb.

API field namesenvelope_ua_btuh_per_degf, capacitance_btu_per_degf, gypsum_lb, wood_lb, concrete_lb, water_lb, indoor_start_degf, outdoor_degf, occupants, other_gains_btuh, first_threshold_degf, second_threshold_degf, time_constant_hours, equilibrium_degf, hours_to_first, hours_to_second, temp_after_24h_degf

• One thermal node room air and structure share one temperature; the first hours fall faster than the curvelumped-capacitance method
• Sensible heat per person about 250 Btu/h at restASHRAE Handbook -- Fundamentals
• Helper specific heats gypsum 0.26, wood 0.3 (low end of 0.3-0.4), concrete 0.2, water 1.0 Btu/lb-degFASHRAE Handbook -- Fundamentals