Conductra

Meet Conductra, a copper rod who passes heat from her hot end to her cold end.

Heat flows on its own from hot to cold. Through a solid it travels by conduction: faster-vibrating atoms and, in metals, free electrons pass energy to their neighbours. In steady state the rate of heat flow through a rod or slab is P = kAΔT/d. It grows with the cross-section area A and the temperature difference ΔT, and falls with the length d.

Materials differ hugely. Copper's thermal conductivity is about 400 W/(m·K); window glass is around 1; still air is about 0.026. A 1 m² glass pane 4 mm thick with a 10 K difference across it would conduct about 1 × 1 × 10 / 0.004 = 2,500 watts if glass alone set the rate.

In practice, thin layers of still air on each surface slow heat flow a lot. That is why double glazing traps air or gas between panes, why down jackets work, and why cooking pans often have copper or aluminium bases.

The formula assumes steady state and a constant k. Real heat flow often involves convection and radiation as well.