Black space capsule

Activity: Black space capsule

Contemporary Challenges 2022 (3 years)

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.

Small Group Activity schedule 30 min. description Student handout (PDF)
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stefan-boltzmann blackbody radiation

This activity follows Using the Stefan-Boltzmann law

You're in charge of designing a black cylindrical space capsule for a manned trip to the Moon. You need a volume you will be comfortable in, and you want the temperature to be cozy. What dimensions should your capsule be (assuming the entire surface is a uniform temperature), and how should it be oriented?

Grey space capsule

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Grey space capsule
Contemporary Challenges 2021 (4 years)
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In this small group activity, students work out the steady state temperature of an object absorbing and emitting blackbody radiation.
Thermal radiation at twice the temperature

Small Group Activity

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Heat shields
Homework

Heat shields
Stefan-Boltzmann blackbody radiation Thermal and Statistical Physics 2020 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.
Blackbody PhET

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Blackbody PhET
Contemporary Challenges 2021 (4 years)
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Acting Out Current Density

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Acting Out Current Density
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Ring Cycle Sequence
Students, pretending they are point charges, move around the room so as to make an imaginary magnetic field meter register a constant magnetic field, introducing the concept of steady current. Students act out linear \(\vec{I}\), surface \(\vec{K}\), and volume \(\vec{J}\) current densities. The instructor demonstrates what it means to measure these quantities by counting how many students pass through a gate.
Ring Cycle Sequence

Sequence

Ring Cycle Sequence
Students calculate electrostatic fields (\(V\), \(\vec{E}\)) and magnetostatic fields (\(\vec{A}\), \(\vec{B}\)) from charge and current sources with a common geometry. The sequence of activities is arranged so that the mathematical complexity of the formulas students encounter increases with each activity. Several auxiliary activities allow students to focus on the geometric/physical meaning of the distance formula, charge densities, and steady currents. A meta goal of the entire sequence is that students gain confidence in their ability to parse and manipulate complicated equations.
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Thermal radiation and Planck distribution
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These notes from the fourth week of Thermal and Statistical Physics cover blackbody radiation and the Planck distribution. They include a number of small group activities.
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Lorentz Transformation (Geometric)
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Basics of heat engines

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Energy radiated from one oscillator

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Learning Outcomes