The house cutaway shows glowing heat particles streaming out through the roof, walls and windows — the brighter and denser the stream, the more heat is escaping through that surface. Each surface has its own U-value (inverse of insulation R-value); windows leak far faster than insulated walls unless upgraded to double glazing. Total heat loss scales with the indoor-outdoor temperature gap, so a colder night or a hotter thermostat setpoint both widen the leaks.
Q = U · A · ΔT (per surface, summed over roof/walls/windows)
U = 1 / R (SI: R in m²·K/W)
cost/day = Q · 24h · electricity_rate / 1000
- Insulation R-value — higher R lowers the wall/roof U-value, throttling the particle stream from those surfaces.
- Thermostat setpoint — raises indoor temperature, widening ΔT and heat loss.
- Outdoor temp — colder outside air widens ΔT the same way.
- Windows toggle — switches between leaky single-pane and efficient double-pane glazing, which cuts window U-value roughly in half.
Real home energy audits use this same Q = U·A·ΔT accounting, surface by surface, to prioritize which upgrade — attic insulation or window replacement — saves the most energy per dollar spent.