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CED objectives

Blackbody Radiation

▶︎  Watch it animatedinteractive step-through · ~3 min · optional ⚙︎  Open the appletBlackbody Bench · move the temperature against a pinned 1500 K curve and commit to which way the peak travels and what the fourth power does

A blackbody's emission curve is fixed by its temperature alone, so two objects at the same temperature glow the same colour whatever they are made of. Wien's law, $\lambda_{\text{max}} T = 2.90\times10^{-3}$ m$\cdot$K, is an inverse relation, so a hotter body peaks at a shorter wavelength and looks bluer. The Stefan-Boltzmann law, $P = \sigma e A T^4$, makes the radiated power scale as the fourth power of the absolute temperature, so tripling the temperature multiplies the power by eighty-one. A blackbody absorbs everything landing on it, and a good absorber is a good emitter.

Three errors dominate. Reading Wien's law as a direct proportion, which pushes the peak toward longer wavelengths as the temperature rises and predicts a heated metal running from white toward red. Scaling the radiated power in proportion to temperature rather than to its fourth power, or raising a Celsius reading to that power. And expecting the emitted spectrum to depend on what the object is made of, or expecting a black surface to emit nothing because black means no light.

raise T: the peak moves LEFT and the area grows as T⁴ power wavelength 3000 K 4500 K 6000 K peaks move this way as T FALLS λ(max) T is a fixed constant, so doubling T halves λ(max): a stove element goes red, orange, white the shape depends on temperature alone: copper and iron at 1200 K glow identically
Two things change together as the temperature rises, and each has its own law: the peak position from Wien and the total area from Stefan-Boltzmann.
P = σeAT⁴: take the ratio with the exponent intact T P 2T 16P 3T 81P scaling linearly turns the bottom bar into three times the top one always in KELVIN: a fourth power of a Celsius reading means nothing. And if the size changes, area goes as r²
Every bar here is the same object at a different temperature. Nothing else about it changed.

The work

3 ways in · any order
Lesson
Blackbody Radiation ›

Reads Wien's law as an inverse relation so hotter means bluer, keeps the fourth power and the kelvin scale in the Stefan-Boltzmann law, and makes the emission curve depend on temperature rather than on the material.

Skill check · 10 scenarios
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Diagnostic
10-item topic check ›

Ten items spanning the failure modes of this topic: pushing the peak toward longer wavelengths as the temperature rises, flattening the fourth power or using Celsius, and expecting the spectrum to depend on the material. Take it cold to find which one is yours, or after the lesson to confirm it is not.

Not started · 10 items · ~15 min
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Targeted Practice
Drill a single misconception ›

Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears it for now and moves you to the next. Two in a row is a checkpoint, not proof: if the error resurfaces later, the misconception comes back.

Take the diagnostic to identify your misconceptions
Diagnostic first