## Activity: Thermal radiation at twice the temperature

Contemporary Challenges 2022 (4 years)
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.
• Media
This small whiteboard question introduces the Stefan-Boltzmann law.
##### Question:
When the temperature of a black surface is doubled, what happens to the total energy emitted per unit time?
1. Increase by 2 times
2. Increase by 4 times
3. Increase by 8 times
4. Increase by 16 times
• group Black space capsule

group Small Group Activity

30 min.

##### 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.
• group Grey space capsule

group Small Group Activity

30 min.

##### Grey space capsule
Contemporary Challenges 2022 (4 years)

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

assignment 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.

• face Review of Thermal Physics

face Lecture

30 min.

##### Review of Thermal Physics
Thermal and Statistical Physics 2020

These are notes, essentially the equation sheet, from the final review session for Thermal and Statistical Physics.
• face Thermal radiation and Planck distribution

face Lecture

120 min.

##### Thermal radiation and Planck distribution
Thermal and Statistical Physics 2020

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.
• computer Blackbody PhET

computer Computer Simulation

30 min.

##### Blackbody PhET
Contemporary Challenges 2022 (4 years)

Students use a PhET to explore properties of the Planck distribution.
• group Energy radiated from one oscillator

group Small Group Activity

30 min.

##### Energy radiated from one oscillator
Contemporary Challenges 2022 (4 years)

This lecture is one step in motivating the form of the Planck distribution.
• face Introducing entropy

face Lecture

30 min.

##### Introducing entropy
Contemporary Challenges 2022 (4 years)

This lecture introduces the idea of entropy, including the relationship between entropy and multiplicity as well as the relationship between changes in entropy and heat.
• face Wavelength of peak intensity

face Lecture

5 min.

##### Wavelength of peak intensity
Contemporary Challenges 2022 (3 years)

This very short lecture introduces Wein's displacement law.
• face Energy and Entropy review

face Lecture

5 min.

##### Energy and Entropy review
Thermal and Statistical Physics 2020 (3 years)

This very quick lecture reviews the content taught in Energy and Entropy, and is the first content in Thermal and Statistical Physics.

Learning Outcomes