### Application of gas laws in atmospheric sciences

This unit provides first tools to describe the atmosphere by means of gas laws, and the vertical profiles of temperature, density, and pressure in a quantitative way, as well as introduces the concept of gravitational force and buoyancy for vertical motions in the atmosphere.

### Learning goal

After this unit, students will be able to

- Apply the gas laws that they already know from physics and/or physical-chemistry to atmospheric sciences
- Apply
*Archimedes law*to an atmospheric column to derive the hydrostatic equation - Develop assumptions to solve a problem and evaluate the consequences of the assumptions
- Evaluate the isothermal atmosphere, homogeneous atmosphere, polytrop atmosphere and US standard atmosphere
- Justify (graduate students only) and apply the derived equations for these atmospheres to solve typical problems

## Students’ Tasks

- Watch this video on the material
It summarizes applying the gas and Archimedes’ laws to the atmosphere and discusses the relation between buoyancy, the ideal gas law, and gravitation in the special cases of the isothermal, homogeneous, and polytrop atmosphere, and the US standard atmosphere.

- Read chapter 2. to 2.3.4 (included) of
*Lectures in Meteorology*. This reading discusses the relation between buoyancy, the ideal gas law, and gravitation. It explains the special cases of the isothermal, homogeneous, and polytrop atmosphere, and the US standard atmosphere, which provide helpful tools for evaluation of the thickness of atmospheric layers, and construction of surface weather maps needed for weather forecast. - Fill out the questionnaire and submit it by 1500 AST the day before class. Part 1 of the questionnaire is P/F and serves to take notes. Part 2 is graded for percentage of correct completion and measures your comprehension of the material. Failure of submission in time leads to an F. Part 3 serves to seek clarification.
- Prepare to present the material to improve your presentation skills. When you are chosen to be the presenter, I will grade your presentation for completeness, and correctness. When you are a graduate student, your presentation as such will be graded too.

### Student Self Assessment of Learning Outcome

Take this quiz to self-assess your knowledge and comprehension. The assigned points add up to 100. Thus, 70 points, for instance, mean you got 70% right. You can find how percentage converts to letter grades in the syllabus.

## Supplementary materials

You can find the powerpoint used in the video here, in case you want to take your notes on the slides.

### FAQ

Q:Where do we apply the hypsometric equation?

**A:** To assess the thickness of the layer between two pressure surface for synoptic purposes.

### Class work

In class, we will work, among other things, on these applications of the gas laws and equations of the isothermal, homogeneous, and polytrop atmosphere.