This activity follows Planck spectral distribution

Google “phet blackbody spectrum”' and open the simulation.

1. 1. At what wavelength is the peak in spectral intensity
      • \(\lambda_{\text{peak}}\) for a black rock on the Earth's surface,
      • \(\lambda_{\text{peak}}\) for the black walls of a pizza oven,
      • \(\lambda_{\text{peak}}\) for a light bulb,
      • \(\lambda_{\text{peak}}\) for the sun.
   2. Check that the peak wavelength decreases with temperature following a \(1/T\) relationship.
2. 1. Use the numerical integration feature (the checkbox labelled “intensity” near the upper-right corner of the graph) to find the total intensity, in units of \(\text{W/m}^2\), emitted by
      • a black rock on the Earth's surface,
      • the black walls of a pizza oven,
      • the surface of a tungsten light bulb filament,
      • the surface of the sun.
   2. Check that these intensities are proportional to \(T^4\). Note, the quick way to check involves ratios: Does \(\frac{I_1}{I_2} = \left(\frac{T_1}{T_2}\right)^4\)?
3. How cold should you make an object if you want zero thermal radiation emitted?
4. (Extra---if your group has time)
   1. For an incandescent light bulb with a filament surface area of \(A\), estimate how efficiently it converts electrical energy into visible photons. Hint: you will need to estimate the following ratio: \begin{align*} \frac{\text{Electromagnetic radiation in visible wavelengths}}{ \text{Total electromagnetic radiation} } = \frac{ A\int_{400\text{ nm}}^{700\text{ nm}} S_\lambda(\lambda, T)d\lambda }{ A\int_{0}^{\infty} S_\lambda(\lambda, T)d\lambda } \end{align*}
   2. Estimate the filament surface area \(A\) for a 60 W light bulb.

These notes from the fourth week of https://paradigms.oregonstate.edu/courses/ph441 cover blackbody radiation and the Planck distribution. They include a number of small group activities.

In this small group activity, students work out the steady state temperature of an object absorbing and emitting blackbody radiation.

This lecture is one step in motivating the form of the Planck distribution.

This small group activity has students reasoning about how the Planck distribution shifts when the temperature is doubled. This leads to a qualitative argument for the Stefan-Boltzmann law.

In this activity, students apply the Stefan-Boltzmann equation and the principle of energy balance in steady state to find the steady state temperature of a black object in near-Earth orbit.

This very short lecture introduces Wein's displacement law.

A black (nonreflective) sheet of metal at high temperature \(T_h\) is parallel to a cold black sheet of metal at temperature \(T_c\). Each sheet has an area \(A\) which is much greater than the distance between them. The sheets are in vacuum, so energy can only be transferred by radiation.

1. Solve for the net power transferred between the two sheets.

2. A third black metal sheet is inserted between the other two and is allowed to come to a steady state temperature \(T_m\). Find the temperature of the middle sheet, and solve for the new net power transferred between the hot and cold sheets. This is the principle of the heat shield, and is part of how the James Web telescope shield works.

3. Optional: Find the power through an \(N\)-layer sandwich.