Heat Transfer · Learn
Every object warmer than absolute zero glows. Here's why emission climbs with the fourth power of temperature, why hotter means bluer, and how two surfaces trade heat across empty space.
Unlike conduction and convection, thermal radiation travels as electromagnetic waves — it crosses a vacuum, which is how the Sun heats the Earth. Every surface both emits radiation (set by its own temperature) and absorbs what arrives from elsewhere.
An idealized blackbody absorbs all incident radiation and emits the maximum possible at every wavelength. Planck's law gives that spectrum — the curve in the lab — and two famous results follow by integrating and differentiating it.
Integrate Planck over all wavelengths and the total emissive power is
That fourth power is everything. Conduction and convection scale roughly with $\Delta T$; radiation with $T^4$. Double the absolute temperature and you radiate 16× as much — negligible at room temperature, utterly dominant in a furnace, a rocket nozzle, or the Sun.
The wavelength of peak emission shifts inversely with temperature:
At 1000 K the peak is deep in the infrared (you feel heat, see nothing); by ~1300 K a little spills into the red; at ~3000 K it's the orange-white of a bulb filament; at 5800 K the peak sits in visible green and the blend reads as white — sunlight.
Real "gray" surfaces emit less than a blackbody by a factor $\varepsilon$ between 0 and 1:
By Kirchhoff's law, a good emitter is a good absorber: at a given wavelength and temperature, $\alpha = \varepsilon$. (This is why a matte-black radiator sheds heat well and a shiny foil — low $\varepsilon$ — makes good insulation.)
When two surfaces face each other, the net transfer depends on geometry through the view factor $F_{12}$ — the fraction of radiation leaving surface 1 that lands on surface 2. In the simple gray limit,
Driven by the difference of fourth powers, so even a modest gap between two hot surfaces moves enormous power. Make $T_2 > T_1$ and the sign flips — surface 1 now gains heat. (For careful work, a radiosity network adds surface resistances $\frac{1-\varepsilon}{\varepsilon A}$ and space resistances $\frac{1}{A_1F_{12}}$ in series.)
Drag $T$ and watch the Wien peak slide toward the visible band while the $\sigma T^4$ area explodes; then set two surfaces against each other and flip the sign of the net exchange. Open the lab →
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