Blackbody spectrum.

Blackbody intensity curves: the peak slides as λ_mT = 2.9 × 10⁻³ m K and the area grows as T⁴, scaled by emissivity.

Set a star so its peak is at 500 nm (≈5800 K), then find the temperature that radiates 16× the power (2T).

Using °C in T⁴; Wien's law giving an interior temperature.

• Radiation needs no medium: heat from the sun crosses the vacuum of space. It travels as electromagnetic waves at 3 × 10⁸ m s⁻¹, and the part emitted because of a body's temperature is called thermal radiation.
• A body that absorbs well also emits well. Black surfaces absorb most of the radiation falling on them; white or shiny surfaces reflect most of it.
• White clothes keep us cooler in summer; dark clothes help in winter. Cooking pots are often blackened at the bottom so that they take in more heat from the fire.
• A thermos (Dewar) flask keeps liquids hot or cold with a double-walled glass vessel. The facing walls are silvered to reflect radiation, the gap between them is evacuated to stop conduction and convection, and the vessel rests on insulating supports such as cork.
• Every body emits radiation over a continuous range of wavelengths. For a blackbody at temperature T the intensity peaks at λ_m given by Wien's displacement law: λ_m T = 2.9 × 10⁻³ m K.
• So a hotter body peaks at a shorter wavelength: iron in a flame glows dull red, then reddish yellow, then white. The moon's peak near 14 μm gives a surface temperature of about 200 K; the sun's peak at 4753 Å gives about 6100 K for its surface, not its interior.
• Blackbody curves depend only on temperature, not on the size, shape or material of the body. Explaining them led to quantum physics.
• Stefan–Boltzmann law: a perfect radiator of area A at absolute temperature T emits H = AσT⁴, with σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴. Real bodies emit H = AeσT⁴, where the emissivity e is between 0 and 1; lamp black comes close to e = 1, a tungsten filament has e ≈ 0.4.
• A body at T in surroundings at T_s also absorbs radiation, so the net loss is H = eσA(T⁴ − T_s⁴).
• A person with skin area 1.9 m², skin at 28 °C (301 K), room at 22 °C (295 K) and e = 0.97 loses H = 0.97 × 5.67 × 10⁻⁸ × 1.9 × (301⁴ − 295⁴) ≈ 66.4 W by radiation, more than half the 120 W the body produces at rest. Arctic clothing adds a thin shiny layer to reflect this radiation back.

Teaching this idea? Put the simulation on your own page or LMS with this code.