The Stefan-Boltzmann law states that the total power a blackbody radiates is proportional to its surface area and the fourth power of its absolute temperature, P = AσT⁴. In AP Physics 2 (Topic 15.4), it explains why hotter objects emit dramatically more electromagnetic energy.
The Stefan-Boltzmann law tells you how much total electromagnetic energy per second (power) a blackbody pumps out, based on just two things, its surface area A and its absolute temperature T. The formula is P = AσT⁴, where σ is the Stefan-Boltzmann constant. A blackbody is an idealized object that absorbs all radiation hitting it, and if it sits in equilibrium at a constant temperature, it must emit energy back out as a continuous spectrum that depends only on its temperature.
The part that matters most is the T⁴. Power doesn't scale with temperature, it scales with temperature to the fourth power. Double the absolute temperature and you don't double the radiated power, you multiply it by 2⁴ = 16. That extreme sensitivity is the whole point of the law, and it's exactly the math AP questions are built around. One catch worth burning into memory is that T must be in kelvins. Celsius will wreck the ratio every time.
This law lives in Topic 15.4: Blackbody Radiation in Unit 15: Modern Physics, supporting learning objective 15.4.A, which asks you to describe the electromagnetic radiation an object emits because of its temperature. The essential knowledge behind it is the idea that matter spontaneously converts internal thermal energy into electromagnetic energy, and a blackbody in equilibrium must emit as much as it absorbs. The Stefan-Boltzmann law is the quantitative half of that story (how MUCH total energy comes out), while Wien's law handles the other half (which wavelength dominates). Blackbody radiation also matters historically. It's the problem classical physics couldn't fully explain, which opened the door to Planck and quantum physics, the central thread of Unit 15.
Keep studying AP® Physics 2 Unit 15
Wien's law (Unit 15)
Wien's law and the Stefan-Boltzmann law are the two outputs of the same blackbody curve. Wien tells you where the peak of the spectrum sits (peak wavelength is inversely proportional to T), while Stefan-Boltzmann tells you the total area under the curve (power goes as T⁴). Exam questions love pairing them, like asking what happens to both the peak wavelength and the total power when temperature doubles.
Planck's law (Unit 15)
Planck's law describes the full shape of the blackbody spectrum, intensity at every wavelength. The Stefan-Boltzmann law is what you get when you add up Planck's curve over all wavelengths. Planck's quantization of energy was the fix for the classical model's failure to match the observed spectrum, the move that kicked off quantum physics.
Continuous spectrum (Unit 15)
A blackbody emits a continuous spectrum, meaning radiation across all wavelengths rather than discrete lines, and that spectrum depends only on temperature. The Stefan-Boltzmann law quantifies the total power carried by that entire continuous spectrum.
Internal energy and thermal equilibrium (Unit 9)
The law is really a thermodynamics idea wearing modern-physics clothes. An object converts internal thermal energy into electromagnetic radiation, and a blackbody at constant temperature must emit energy at the same rate it absorbs it. That equilibrium logic comes straight from the energy-conservation thinking you built in thermodynamics.
Stefan-Boltzmann questions are almost always ratio problems. A typical multiple-choice stem gives you two blackbodies at different temperatures, say 3000 K and 6000 K, and asks for the ratio of their radiated powers. The temperature ratio is 2, so the power ratio is 2⁴ = 16. Another classic doubles the temperature (T₂ = 2T₁) and asks what happens to both the peak wavelength (it halves, by Wien's law) and the total power (it jumps by a factor of 16). Star questions show up too. A blue star versus a yellow 6000 K star tests whether you can connect color to temperature and temperature to how rapidly thermal energy converts into electromagnetic radiation. Watch for problems where surface area differs as well, since P depends on A, not just T. No released FRQ has used this term verbatim, but the underlying skill, reasoning about how P scales with T, is fair game in any quantitative blackbody question.
Both laws come from the same blackbody spectrum, so it's easy to grab the wrong one. The Stefan-Boltzmann law answers "how much total power is radiated?" and scales as T⁴ (hotter means way more energy). Wien's law answers "which wavelength is brightest?" and scales as 1/T (hotter means the peak shifts to shorter, bluer wavelengths). Quick check: if the question says power, intensity, or energy per second, use Stefan-Boltzmann. If it says peak wavelength, maximum intensity wavelength, or color, use Wien.
The Stefan-Boltzmann law, P = AσT⁴, says the total power radiated by a blackbody is proportional to its surface area and the fourth power of its absolute temperature.
Because of the T⁴ dependence, doubling the absolute temperature multiplies the radiated power by 16, not by 2.
Temperature must be in kelvins (absolute temperature), or every ratio calculation will come out wrong.
A blackbody in equilibrium at constant temperature must emit energy at the same rate it absorbs it, and its emitted spectrum depends only on temperature.
Stefan-Boltzmann gives total power (the area under the blackbody curve), while Wien's law gives the peak wavelength (where the curve is tallest), and exam questions often test both in one problem.
Hotter objects radiate more total power and shift their peak emission toward shorter wavelengths, which is why a blue star is hotter than a yellow one.
It's the law that the total power radiated by a blackbody equals its surface area times the Stefan-Boltzmann constant times its absolute temperature to the fourth power, P = AσT⁴. It appears in Topic 15.4 (Blackbody Radiation) under learning objective 15.4.A.
No. Power scales with the fourth power of absolute temperature, so doubling T multiplies the radiated power by 2⁴ = 16. This is the single most-tested fact about the law, like comparing blackbodies at 3000 K and 6000 K.
Stefan-Boltzmann gives the total power radiated (proportional to T⁴), while Wien's law gives the wavelength of maximum intensity (proportional to 1/T). If the question asks about power or energy per second, use Stefan-Boltzmann; if it asks about peak wavelength or color, use Wien.
Yes. T must be absolute temperature in kelvins because the law depends on T⁴, and Celsius values destroy the ratio. A jump from 27°C to 327°C is really 300 K to 600 K, a power increase of 16 times.
A blue star's peak emission sits at a shorter wavelength, which by Wien's law means a higher surface temperature than a yellow star's roughly 6000 K. By the Stefan-Boltzmann law, that higher temperature means it converts thermal energy into electromagnetic radiation at a much greater rate, since power scales as T⁴.
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