## Activity: Optical depth of atmosphere

Contemporary Challenges 2022 (4 years)
In this activity students estimate the optical depth of the atmosphere at the infrared wavelength where carbon dioxide has peak absorption.

This activity follows Temperature of the Earth.

Estimate the optical depth for infrared light with wavelength 15 $\mu$m when it travels through our atmosphere at standard temperature and pressure $STP$. The number density of air molecules at STP can be found from $pV=Nk_BT$.

Our air is 0.041% CO2 (410 ppm).

• assignment The puddle

assignment Homework

##### The puddle
differentials Static Fields 2022 (4 years) The depth of a puddle in millimeters is given by $h=\frac{1}{10} \bigl(1+\sin(\pi xy)\bigr)$ Your path through the puddle is given by $x=3t \qquad y=4t$ and your current position is $x=3$, $y=4$, with $x$ and $y$ also in millimeters, and $t$ in seconds.
1. At your current position, how fast is the depth of water through which you are walking changing per unit time?
2. At your current position, how fast is the depth of water through which you are walking changing per unit distance?
3. FOOD FOR THOUGHT (optional)
There is a walkway over the puddle at $x=10$. At your current position, how fast is the depth of water through which you are walking changing per unit distance towards the walkway.
• 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.
• assignment Find Force Law: Logarithmic Spiral Orbit

assignment Homework

##### Find Force Law: Logarithmic Spiral Orbit
Central Forces 2023 (3 years)

In science fiction movies, characters often talk about a spaceship “spiralling in” right before it hits the planet. But all orbits in a $1/r^2$ force are conic sections, not spirals. This spiralling in happens because the spaceship hits atmosphere and the drag from the atmosphere changes the shape of the orbit. But, in an alternate universe, we might have other force laws.

Find the force law for a mass $\mu$, under the influence of a central-force field, that moves in a logarithmic spiral orbit given by $r = ke^{\alpha \phi}$, where $k$ and $\alpha$ are constants.

• group de Broglie wavelength after freefall

group Small Group Activity

30 min.

##### de Broglie wavelength after freefall
Contemporary Challenges 2022 (4 years)

In this activity students combine energy conservation with the relationship between the de Broglie wavelength and momentum to find the wavelength of atoms that have been dropped a given distance.
• assignment Calculation of $\frac{dT}{dp}$ for water

assignment Homework

##### Calculation of $\frac{dT}{dp}$ for water
Clausius-Clapeyron Thermal and Statistical Physics 2020 Calculate based on the Clausius-Clapeyron equation the value of $\frac{dT}{dp}$ near $p=1\text{atm}$ for the liquid-vapor equilibrium of water. The heat of vaporization at $100^\circ\text{C}$ is $2260\text{ J g}^{-1}$. Express the result in kelvin/atm.
• assignment Find Force Law: Spiral Orbit

assignment Homework

##### Find Force Law: Spiral Orbit
Central Forces 2023 (3 years)

In science fiction movies, characters often talk about a spaceship “spiralling in” right before it hits the planet. But all orbits in a $1/r^2$ force are conic sections, not spirals. This spiralling in happens because the spaceship hits atmosphere and the drag from the atmosphere changes the shape of the orbit. But, in an alternate universe, we might have other force laws.

Find the force law for a central-force field that allows a particle to move in a spiral orbit given by $r=k\phi^2$, where $k$ is a constant.

• face A coarse-grained model for transportation

face Lecture

30 min.

##### A coarse-grained model for transportation
Contemporary Challenges 2022 (4 years)

A short lecture introducing the idea that most of the energy loss when driving is going into the kinetic energy of the air.
• face Energy and heat and entropy

face Lecture

30 min.

##### Energy and heat and entropy
Energy and Entropy 2021 (2 years)

This short lecture introduces the ideas required for Ice Calorimetry Lab or Microwave oven Ice Calorimetry Lab.
• face Chemical potential and Gibbs distribution

face Lecture

120 min.

##### Chemical potential and Gibbs distribution
Thermal and Statistical Physics 2020

These notes from the fifth week of Thermal and Statistical Physics cover the grand canonical ensemble. They include several small group activities.
• assignment Derivatives from Data (NIST)

assignment Homework

##### Derivatives from Data (NIST)
Energy and Entropy 2021 (2 years) Use the NIST web site “Thermophysical Properties of Fluid Systems” to answer the following questions. This site is an excellent resource for finding experimentally measured properties of fluids.
1. Find the partial derivatives $\left(\frac{\partial {S}}{\partial {T}}\right)_{p}$ $\left(\frac{\partial {S}}{\partial {T}}\right)_{V}$ where $p$ is the pressure, $V$ is the volume, $S$ is the entropy, and $T$ is the temperature. Please find these derivatives for one gram of methanol at one atmosphere of pressure and at room temperature.
2. Why does it take only two variables to define the state?
3. Why are the derivatives above different?
4. What do the words isobaric, isothermal, and isochoric mean?

Learning Outcomes