### 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. **ATM401:**Fill out the questionnaire and submit it by Thursday 2359 AST. 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 and is not graded.**ATM601/CHEM601:**Write a brief summary of the read material and submit your summary and answer the questions in this form by Thursday 2359 AST. Part 1 of the form is P/F. 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 and is not graded.**All students:**Download this Unit 2 task sheet with applications of the gas laws and equations of the isothermal, homogeneous, and polytrop atmospheres. Solve the problems that apply to the class you take. This means when you take the class as ATM401, only the problems indicated for ATM401 and “all students” are mandatory for you. When you take the class at ATM601 or CHEM601 only the problems indicated as such and for all students are mandatory. Your solutions should clearly show how you got to your results. Once you are done with the tasks, scan them in and save each problem solution as one PDF file with your name and the unit indicated. If I, for instance, would submit my solution of problem 1, the name of the PDF-file would be Nicole-Mölders-unit-2-problem-1.pdf. Submit your scanned in PDF solutions file here. Don’t know how the create a pdf-file? Go to the FAQ for help.

## Supplementary materials

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

### 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.

### FAQ

Q:Where do we apply the hypsometric equation?

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

Q:Is the individual gas constants of moist air and the same as the individual gas constant of water vapor?

No. The individual gas constant of water vapor is 461 J/(kg K) and relates to the water vapor as the only gas. On the contrary, the individual gas constant of moist air relates to a mixture of gases that among other species includes a certain fraction of water vapor. The individual gas constant of moist air has always to be calculated depending on the fraction of water vapor that the moist air holds.

Q:What’s the difference between the US standard atmosphere and a polytrop atmosphere?

**A:** The US standard atmosphere is a hypothetical vertical distribution of atmospheric temperature, pressure, and density that serves as a representative atmosphere for pressure altimeter calibrations, ballistic tables, design of aircraft and missiles, aircraft performance calculations and alike. For more information see the AMS glossary. A polytrop atmosphere is a real atmosphere. For a comparison see the diagram below.