## Activity: A coarse-grained model for transportation

Contemporary Challenges 2021 (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.
• Media

• The same model used in MacKay's book
• Introduce key ideas from thermodynamics
• A valuable model for figuring out how we're going to save the Earth
Let's start by visualizing the energy flow associated with driving a gasoline-powered car. We will use a box and arrow diagram, where boxes represent where energy can accumulate, and arrows show energy flow.

The energy clearly starts in the form of gasoline in the tank. Where does it go?

The heat can look like

• Hot exhaust gas
• The radiator (its job is to dissipate heat)
• Friction heating in the drive train

The work contribute to

• Rubber tires heated by deformation
• Wind, which ultimately ends up as heating the atmosphere

The most important factors for a coarse-grain model of highway driving:

1. The 75:25 split between “heat” and “work”
2. The trail of wind behind a car
What might we have missed? Where else might energy have gone? We ignored the kinetic energy of the car, and the energy dissipated as heat in the brakes. On the interstate this is appropriate, but for city driving the dominant “work” may be in accelerating the car to 30 mph, and with that energy then converted into heat by the brakes.

• face Basics of heat engines

face Lecture

10 min.

##### Basics of heat engines
Contemporary Challenges 2021 (4 years) This brief lecture covers the basics of heat engines.
• assignment Power from the Ocean

assignment Homework

##### Power from the Ocean
heat engine efficiency Energy and Entropy 2021 (2 years)

It has been proposed to use the thermal gradient of the ocean to drive a heat engine. Suppose that at a certain location the water temperature is $22^\circ$C at the ocean surface and $4^{o}$C at the ocean floor.

1. What is the maximum possible efficiency of an engine operating between these two temperatures?

2. If the engine is to produce 1 GW of electrical power, what minimum volume of water must be processed every second? Note that the specific heat capacity of water $c_p = 4.2$ Jg$^{-1}$K$^{-1}$ and the density of water is 1 g cm$^{-3}$, and both are roughly constant over this temperature range.

• group Energy radiated from one oscillator

group Small Group Activity

30 min.

##### Energy radiated from one oscillator
Contemporary Challenges 2021 (4 years)

This lecture is one step in motivating the form of the Planck distribution.
• group Black space capsule

group Small Group Activity

30 min.

##### Black space capsule
Contemporary Challenges 2021 (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 Earthquake waves

group Small Group Activity

30 min.

##### Earthquake waves
Contemporary Challenges 2021 (4 years)

In this activity students use the known speed of earthquake waves to estimate the Young's modulus of the Earth's crust.
• face Wavelength of peak intensity

face Lecture

5 min.

##### Wavelength of peak intensity
Contemporary Challenges 2021 (3 years)

This very short lecture introduces Wein's displacement law.
• group Thermal radiation at twice the temperature

group Small Group Activity

10 min.

##### Thermal radiation at twice the temperature
Contemporary Challenges 2021 (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.
• face Equipartition theorem

face Lecture

30 min.

##### Equipartition theorem
Contemporary Challenges 2021 (4 years)

This lecture introduces the equipartition theorem.
• group Hydrogen emission

group Small Group Activity

30 min.

##### Hydrogen emission
Contemporary Challenges 2021 (5 years)

In this activity students work out energy level transitions in hydrogen that lead to visible light.
• group de Broglie wavelength after freefall

group Small Group Activity

30 min.

##### de Broglie wavelength after freefall
Contemporary Challenges 2021 (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.

Learning Outcomes