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Instructor notes: Blackbody Radiation: Thermal Spectrum and Temperature

Public notes (v0.2 policy). Not linked from primary navigation.

Exhibit: /cosmic-playground/exhibits/blackbody-radiation/

Overview

Navigation

This guide is instructor-facing Student demo: /play/blackbody-radiation/
Main code: apps/demos/src/demos/blackbody-radiation/main.ts
Model code: packages/physics/src/blackbodyRadiationModel.ts

Where to go next

  • Model + math + assumptions: model.md
  • In-class activities (MW + Friday lab + station version): activities.md
  • Assessment bank (clickers + short answer + exit ticket): assessment.md
  • Future enhancements (planning backlog): backlog.md

Why this demo exists

Why This Matters “Color” is one of the most information-dense measurements we can make in astronomy. This demo helps students build the correct mapping between temperature and the spectrum of thermal light: hotter objects emit more light overall and peak at shorter wavelengths. That turns an observable (spectrum/color) into a physical inference (temperature, and—when combined with radius—luminosity).

This demo makes the Observable → Model → Inference pattern explicit:

  • Observable: the shape and peak position of a spectrum as temperature changes.
  • Model: blackbody radiation laws (Planck shape; Wien peak shift; Stefan–Boltzmann total power).
  • Inference: star temperature (and how “red vs blue” in astronomy reverses everyday fire intuition).

Learning goals (ASTR 101)

By the end of this demo, students should be able to:

  • State the qualitative rules: hotter → peak at shorter wavelength (“bluer” peak) and larger total emitted power.
  • Explain why “red” stars are cooler than “blue” stars (astronomy vs fire analogy).
  • Recognize stars as approximate blackbodies (useful first model).
  • Use the visible band highlight to explain why some objects are “invisible” to our eyes but visible to IR telescopes.

Learning goals (ASTR 201 stretch)

Students should be able to:

  • Use Wien’s law $\lambda_{\text{peak}} \propto 1/T$ to reason about how peak wavelength shifts.
  • Use Stefan–Boltzmann scaling $F \propto T^4$ to compare total emitted power per unit area.
  • Connect temperature + radius to luminosity conceptually ($L \propto R^2 T^4$).

10–15 minute live-teach script (projector)

  1. Start with a prediction rooted in everyday intuition. Ask: “In everyday life, red things feel hot (fire, stove coils). In astronomy, do you think red stars are hotter or cooler than blue stars?” Collect predictions.

  2. Anchor with a familiar reference. Click the Sun preset and point out the visible-band highlight and the peak marker. Ask: “If we could see from space, would the Sun look yellow or closer to white?” Use this as a setup for “our atmosphere/eyes bias what ‘color’ feels like.”

  3. Change temperature and watch two things at once. Move to a cooler preset (e.g., M dwarf) and ask students to predict what happens to:

    • the peak wavelength location, and
    • the overall height/area of the curve. Then reveal and narrate: cooler → peak shifts to longer wavelengths and total emission drops.

  4. Then go hotter. Click the A/B star preset. Ask: “Should the peak move toward the UV or toward the IR?” Confirm with the peak marker and the visible-band highlight.

  5. Compare two temperatures using the instrument workflow. Add two rows in Station mode (or copy results twice) and ask: “If temperature doubles, what happens to the peak wavelength?” (Half) and “What happens to total emitted power per area?” (Grows dramatically; connect to $T^4$ qualitatively.)

  6. Close with inference. Say explicitly: “Color/spectrum is an observable. A model turns that into a temperature inference. Then temperature plus other measurements supports higher-level stories: stellar types, star formation, and what we can detect.”

Misconceptions + prediction prompts

Use these to trigger cognitive conflict:

  • Misconception: “Red means hot.”
    Prompt: “If ‘red = hot,’ then would a red star be more energetic than a blue star?” Use the spectrum peak shift to show red stars peak at longer wavelengths (cooler).

  • Misconception: “Blue stars are young.”
    Prompt: “What physical property does this demo actually control?” (Temperature.) Emphasize: color ↔ temperature; age is a separate inference.

  • Misconception: “The Sun is yellow.”
    Prompt: “What does the spectrum say about where the Sun emits most strongly?” Use the peak marker and the visible band highlight to separate “spectrum” from “how it looks from Earth.”

  • Misconception: “Infrared means ‘heat’ (only).”
    Prompt: “If IR is ‘heat,’ what would it mean to say the Sun emits infrared?” Reinforce: thermal radiation spans bands; IR telescopes help because cooler objects peak there.

Suggested connections to other demos

  • EM spectrum: puts wavelength bands in context; helps students interpret “peak in UV” vs “peak in IR.”
  • Telescope resolution: observing in the infrared changes resolution for a given aperture; tie “why JWST is IR” to what tradeoffs it accepts.

Activities

Navigation

MW Quick (3–5 min)

Type: Demo-driven
Goal: Flip the “red = hot” intuition using prediction-first evidence.

  1. Open: /play/blackbody-radiation/
  2. Click the M dwarf preset. Ask: “Hotter or cooler than the Sun?” (Prediction.)
  3. Click Sun. Ask again: “Which is hotter: Sun or M dwarf?”
  4. Reveal with the temperature readout and the spectrum peak position. Say explicitly: in astronomy, redder stars are cooler.
  5. 20-second debrief: “Color is an observable; the blackbody model connects it to temperature.”

MW Short (8–12 min)

Type: Demo-driven (pairs)
Goal: Empirically discover Wien scaling (peak shifts) without “plug-and-chug.”

Student task (pairs)

  1. Start at Sun.
  2. Record:
    • temperature $T$,
    • peak wavelength $\lambda_{\text{peak}}$ (use the peak marker),
    • a short description of which band dominates (visible vs IR vs UV/microwave).
  3. Change to a cooler preset (M dwarf) and a hotter preset (A/B star).
  4. Answer (in words): “When $T$ increases, what happens to $\lambda_{\text{peak}}$? What happens to the area under the curve?”

Optional quantitative check (2 min): pick two temperatures where one is about $2\times$ the other and see whether $\lambda_{\text{peak}}$ is about half (Wien scaling).

Friday Lab (20–30+ min)

Type: Demo-driven investigation (small groups)
Goal: Build a claim–evidence model: temperature controls both peak wavelength and total emitted power.

Driving questions

  1. How does $\lambda_{\text{peak}}$ depend on $T$?
  2. How does the total emitted power per area depend on $T$?

Protocol

  1. Choose 5 temperatures spanning the slider range (record them).
  2. For each temperature, record:
    • $\lambda_{\text{peak}}$ from the peak marker/readout,
    • the luminosity/flux indicator readout (if shown) or a qualitative “more/less area” statement.
  3. Make two claims with evidence:
    • Claim A (Wien): “Hotter → peak shifts to shorter wavelength.”
    • Claim B (Stefan): “Hotter → much more total emission.”
  4. Write one paragraph connecting the results to stellar color:
    • “Why are cool stars red?”
    • “Why might cool objects be ‘invisible’ to our eyes but visible in IR?”

Extension (if time)

Use the log vs linear display toggle and discuss: “Which view makes the long-wavelength tail easier to see, and why might astronomers like log plots?”

Station version (6–8 min)

Station card: Blackbody Radiation (6–8 minutes) Pick one preset (M dwarf, Sun, A/B star, or CMB) and record:

  • Temperature $T$ (K)
  • Peak wavelength $\lambda_{\text{peak}}$ (nm)
  • Which band dominates (IR / visible / UV / microwave)

Then write one sentence:

“This star looks ____ because its blackbody peak is at ____.”

Word bank + sanity checks Word bank:

  • Blackbody spectrum: the ideal “thermal glow” curve; temperature sets its shape.
  • Temperature $T$ (K): hotter objects emit more and peak at shorter wavelengths.
  • Peak wavelength $\lambda_{\text{peak}}$: where the curve is highest (the “peak marker”).

Key relationship (Wien scaling):

$$\lambda_{\text{peak}} \propto \frac{1}{T}$$

Sanity checks:

  • Hotter → $\lambda_{\text{peak}}$ shifts to shorter wavelength (toward blue/UV).
  • Cooler → $\lambda_{\text{peak}}$ shifts to longer wavelength (toward red/IR).
  • In astronomy, “redder” blackbodies are cooler, not hotter.

Assessment

Navigation

Clicker questions (with distractors + explanation)

Clicker 1 — Which is hotter?

Demo setup: open /play/blackbody-radiation/ and compare presets M dwarf and A/B star.

Question: Which object is hotter?

A. M dwarf
B. A/B star
C. Same temperature
D. You can’t tell from the spectrum

Correct: B
Why: Hotter blackbodies peak at shorter wavelengths and the temperature readout confirms the preset ordering.
Misconception targeted: “Red means hot.”

Clicker 2 — Peak shift (Wien scaling)

Demo setup: start at Sun; then increase temperature.

Question: As temperature increases, the peak wavelength $\lambda_{\text{peak}}$…

A. shifts to longer wavelength (redder)
B. shifts to shorter wavelength (bluer)
C. stays fixed
D. disappears

Correct: B
Why: Wien’s law: $\lambda_{\text{peak}} \propto 1/T$.
Misconception targeted: confusing “red hot” everyday intuition.

Clicker 3 — Total power scaling (qualitative)

Demo setup: compare two temperatures (any two distinct settings).

Question: If a star’s temperature increases (same size), its emitted power per unit area…

A. decreases
B. increases slowly (roughly linear in $T$)
C. increases very steeply (roughly like $T^4$)
D. stays the same

Correct: C
Why: Stefan–Boltzmann scaling $F \propto T^4$ (the curve’s overall “area” grows rapidly).
Misconception targeted: underestimating temperature’s impact on luminosity.

Clicker 4 — Visible vs infrared detectability

Demo setup: set temperature to a low value (or use a cool preset like CMB).

Question: A very cool object’s blackbody peak is most likely in:

A. X-ray
B. Visible
C. Infrared / microwave
D. Ultraviolet

Correct: C
Why: Cooler → longer peak wavelength. The demo shows cool spectra peaking outside visible.
Misconception targeted: “If we can’t see it with eyes, it isn’t emitting.”

Clicker 5 — The Sun’s “color”

Demo setup: select Sun.

Question: Which statement best matches the model?

A. The Sun emits only yellow light.
B. The Sun peaks in the visible and emits across the whole visible band, so from space it appears close to white.
C. The Sun is red because it’s cooler than other stars.
D. Color is unrelated to temperature.

Correct: B
Why: The spectrum is broad across visible even if there is a peak; the demo’s insight text and curve support this.
Misconception targeted: “The Sun is yellow” as a hard physical statement.

Clicker 6 — What does “blackbody” mean here?

Demo setup: none.

Question: In this demo, treating a star as a blackbody means:

A. It emits no light.
B. Its emitted spectrum depends mainly on temperature, even though real stars also show spectral lines.
C. It absorbs no light.
D. Only black-colored objects behave this way.

Correct: B
Why: Blackbody is an idealized thermal emitter model; it’s a useful first approximation.
Misconception targeted: literal interpretation of the word “black.”

Short-answer prompts

  1. Explain why “red hot” is a misleading phrase for stars.
  2. Using the demo, describe two ways the spectrum changes when temperature increases.
  3. Why might an infrared telescope be better than a visible telescope for finding cool objects (brown dwarfs, dust)?
  4. In one paragraph: how does blackbody radiation support the idea that astronomy infers physical properties from light?

Exit ticket (3 questions)

  1. Hotter objects peak at (shorter/longer) wavelengths.
  2. If temperature doubles, does total emitted power per unit area increase by about $2\times$, $4\times$, $8\times$, or $16\times$?
  3. Name one common misconception about star color and temperature.

Model notes (deeper)

Navigation

Links Student demo: /play/blackbody-radiation/
Model code: packages/physics/src/blackbodyRadiationModel.ts
UI/visualization code: apps/demos/src/demos/blackbody-radiation/main.ts

What the demo is modeling (big picture)

This demo models the spectrum of an idealized blackbody: an object that absorbs all incident radiation and emits a temperature-dependent spectrum of thermal light. The UI is built to highlight three linked ideas:

  • Shape: the Planck curve has a steep short-wavelength side and a long tail.
  • Peak shift: hotter objects peak at shorter wavelengths (Wien’s law).
  • Total power: hotter objects emit dramatically more energy per unit area (Stefan–Boltzmann law).

The model computations live in packages/physics/src/blackbodyRadiationModel.ts and are used by the interactive view in apps/demos/src/demos/blackbody-radiation/main.ts.

Units + conventions used in the code

The shared model uses CGS internally:

  • Wavelength $\lambda$ in cm
  • Temperature $T$ in K
  • Spectral radiance $B_\lambda$ in erg/s/cm^2/sr/cm (theoretical units; the UI may plot in relative scaling for readability)

Key constants (as implemented in packages/physics/src/blackbodyRadiationModel.ts):

  • $c = 2.998\times 10^{10}\ \text{cm/s}$
  • $h = 6.626\times 10^{-27}\ \text{erg·s}$
  • $k_B = 1.381\times 10^{-16}\ \text{erg/K}$
  • $\sigma = 5.670\times 10^{-5}\ \text{erg}/(\text{cm}^2\cdot\text{s}\cdot\text{K}^4)$
  • $b = 0.2898\ \text{cm·K}$ (Wien displacement constant in cm·K)

Key relationships to foreground (with meaning + units)

Wien’s displacement law: peak wavelength vs temperature

$$\lambda_{\text{peak}} = \frac{b}{T}$$

Let’s unpack each piece:

  • $\lambda_{\text{peak}}$ is the wavelength of peak emission (cm).
  • $b$ is Wien’s displacement constant (cm·K).
  • $T$ is temperature (K).

What this equation is really saying: hotter objects peak at shorter wavelengths.

Sanity checks

  • Units: (cm·K)/K = cm ✓
  • Scaling: if $T$ doubles, $\lambda_{\text{peak}}$ halves ✓

Stefan–Boltzmann law: total emitted flux vs temperature

$$F = \sigma T^4$$

Let’s unpack each piece:

  • $F$ is total emitted energy per unit area per unit time (erg/s/cm^2).
  • $\sigma$ is the Stefan–Boltzmann constant.
  • $T$ is temperature (K).

What this equation is really saying: temperature has a very steep effect on total power output per unit area.

Sanity checks

  • Scaling: if $T$ doubles, $F$ increases by $2^4 = 16$ ✓

Planck function: the full spectrum shape (optional deep dive)

$$B_\lambda(T) = \frac{2hc^2}{\lambda^5}\cdot\frac{1}{e^{hc/(\lambda k_B T)} - 1}$$

Let’s unpack each piece (conceptually):

  • The prefactor $2hc^2/\lambda^5$ sets the overall scaling and pushes the curve down at long wavelengths.
  • The exponential term sets the sharp cutoff at short wavelengths.

For teaching, you usually do not need students to memorize this. The demo uses it to generate the characteristic curve and then uses Wien + Stefan as the interpretable “handles.”

Assumptions, limitations, and sanity checks

  • The model assumes an ideal blackbody (emissivity = 1). Real stars are approximate blackbodies with spectral lines superimposed.
  • The temperature-to-color display is a perceptual approximation, not full colorimetry (temperatureToColor is explicitly documented as approximate in the model).
  • Numerical stability: the implementation clips extreme exponents (e.g., returns 0 when the Planck exponent is very large) to avoid overflow.

Backlog

Navigation

P0 (blocking / correctness / teachability)

  • Optional compare UX: decide whether to add an explicit compare overlay beyond the current workflow (Station mode rows / copy-results comparisons).
  • Instructor usability: add a one-page “teach script + misconceptions + one key question” printable summary linked from the instructor guide.
  • CMB storyline (optional): decide whether CMB presets are in-scope for ASTR 101 and, if so, add a short instructor-note section on how/when to use them.

P1 (important)

  • Stefan–Boltzmann intuition: add an “area under the curve” visualization toggle (matches README future ideas) to make $T^4$ scaling more visceral.
  • Approximations clarity: keep “temperature → color” language explicitly perceptual/approximate (see packages/physics/src/blackbodyRadiationModel.ts notes).
  • Answer keys: add suggested “ideal student responses” to the activities protocols to reduce TA variability.

P2 (nice to have)

  • Model extensions (from README ideas): Wien/Rayleigh-Jeans/Wien approximations overlay; real stellar spectra comparison (absorption lines); HR-diagram connection.
  • Practice mode: lightweight “guess the temperature from the curve” quiz mode.