Building Energy Model for an energy audit

Heat flows through a wall like current through resistors in series. Each layer's thermal resistance is its thickness over its conductivity; adding them gives the total R-value, and the heat flux is the temperature difference divided by it. Insulation, with very low conductivity, dominates the R-value — the steep temperature drop shows where it does its work.

A solar array's output is its rated power (area × efficiency at 1000 W/m²) multiplied by the peak sun hours your location receives — the equivalent full-intensity hours per day. Tilt matters too: aiming the panels near your latitude maximizes annual yield. Real systems lose a bit more to heat, wiring, and inverters.

A heat pump does not make heat — it moves it, so it can deliver several kilowatts of warmth per kilowatt of electricity. The coefficient of performance is that ratio, capped by the Carnot limit T_hot/(T_hot − T_cold). The colder it gets outside, the harder the pump works and the lower the COP — but even at freezing it beats a resistance heater several times over.

LCOE spreads a power project's lifetime cost over every megawatt-hour it produces, letting wildly different technologies be compared fairly. It rewards high capacity factors and cheap capital, and punishes idle plants. The capital-recovery factor discounts future costs to today. It is the number that has made solar and wind the cheapest new power in most of the world.