METEO 431 Atmospheric Thermodynamics

ATMOSPHERIC THERMODYNAMICS Instructor: Peter R. Bannon Lectures: Mon., Wed. & Fri. 12:20-1:10 p.m. 105 Walker BuildingTeaching Assistant: Scott Loeffler


Classical thermodynamics applied to both the dry and the moist atmosphere.

Required course for Meteo Majors. 

Course Structure 

Examinations:  Two midterms and a final exam are planned.  The midterms are tentatively scheduled during class on October 9th and November 13th.  Each mid-term will contribute 22.5% to your final grade, the comprehensive final, given during finals week, 40%. 

Problem Sets:  Frequent problem sets will be given.  The problem sets are due every Wednesday.  Together the problem sets will count towards 15% of your grade. 


  1. Student participation in class is essential.  Bonus points of up to 5% of your grade will be assigned based on your individual level of participation.  Anyone who misses class regularly without a reasonable excuse is, of course, unlikely to receive these points.
  2. Final grades are assigned on a curve with the average grade being a B/B-.  Students lying one standard deviation below the mean are in jeopardy of receiving a grade of D or F.
  3. 20% penalty for problem sets turned in after 4:30 p.m. on the due date.
  4. No problem sets will be accepted after the answers are posted or discussed in class.
  5. Make-up exams by prior arrangement only.
  6. No make-up final except for a direct conflict. 

Prerequisites: Phys 212 is required; Math 140, 141, and Meteo 300 are recommended. 

Textbooks:  Atmospheric Thermodynamics by Bohren and Albrecht. 

Lectures: Mon., Wed. & Fri. 12:20-1:10 p.m. 105 Walker Building 

521 Walker Building

Office hours:  Mon. Wed. & Fri. 1:30-2:30 p.m., by appointment, or whenever the door is open 

Teaching Assistant:         
530 Walker Building 

Office hours: TBA 

Course Outline:

The outline for the course follows.  Please note that this outline serves only as a general guide to the course. The actual topics covered may vary at the discretion of the instructor.



  1. Introduction         
  2. Energy: First Law of Thermodynamics 
    • Newton’s second law: Momentum and forces
    • Kinetic and potential energies of a point mass: Work
    • A system of point masses: Internal energy
    • Conservation of energy
    • First law: Working and heating 
  3. Air
    • Ideal gas law
    • Kinetic theory of gases
    • Hydrostatic relation
    • Mixture of gases: Dalton’s law
    • Kinetic theory II: Collisions
    • Van der Waals gas 
  4. Atmospheric Applications of the First Law
    •    Working
    •    Heating at constant pressure and constant volume:  Specific heats
    •    Enthalpy
    •    Adiabatic processes: Potential temperature, dry adiabatic lapse rate
    •    Static stability: Buoyancy
    •    Heat engines: Carnot cycle
    •    Thermodynamic diagrams: dry skew T – log p  
  5. Entropy: Second Law of Thermodynamics
    • Spontaneous change
    • Energy degradation
    • Early statements of the second law
    • Reversible vs. irreversible processes
    • Entropy and the second law 
  6. Water: Phase Changes
    •  States of matter: Liquid, solid, and gas
    • Intermolecular forces
    • Condensation and evaporation: A molecular perspective
    • Thermodynamics of phase changes
    • Clausius-Clapeyron equations
    • Phase diagrams
  7. Moist Air 
    • Moisture variables
    • Moist equations of state
    • Moist isobaric processes
    • Moist adiabatic processes
  8. Thermodynamics of Clouds
    •  Level of cloud formation
    • Saturated adiabatic processes
    • Thermodynamic diagrams: moist/saturated skew T – log p
    • Conditional instability: LCL, LFC, and LNB
    • Parcel energetics: CAPE and CIN
    • Entrainment



  • Ambaum, M. H. P., 2010: Thermal Physics of the Atmosphere. Wiley-Blackwell, 239 pp. QC880.4.T5A43B 2010 
  • *Bohren, C. F., and B. A. Albrecht, 1998: Atmospheric Thermodynamics. New York: Oxford University Press, 402 pp. QC880.4.T5B63 1998 
  • Curry, J. A., and P. J. Webster, 1999: Thermodynamics of Atmospheres and Oceans.  New York, Academic Press, 471 pp. QC880.4.T5C87 1999
  • Dutton, J. A., 1995: Dynamics of Atmospheric Motion (formerly The Ceaseless Wind.)   New York, Dover, 617 pp.  Chapters 3 and 8.  QC880.4.A8D88 1995
  • Emanuel, K. A., 1994: Atmospheric Convection.  Oxford University Press, 580 pp.   QC880.4.C64E5 1994
  • Fenn, J. B., 1982: Engines, Energy, and Entropy: A Thermodynamics Primer. Global View, 293. TJ265.F37
  • Miller, S., 2015: Applied Thermodynamics for Meteorologists. New York, Cambridge University Press, 385 pp.
  • North, G. R., and T. L. Erukhimova, 2009: Atmospheric Thermodynamics: Elementary Physics and Chemistry. Cambridge, 267 pp.  QC880.4.T5N67
  • *Petty, G. W., 2008: A First Course in Atmospheric Thermodynamics. Sundog Publishing, 336 pp. QC880.4.T5P48 2008
  • Tsonis, A. A., 2007: An Introduction to Atmospheric Thermodynamics. Second Edition. Cambridge University Press, 171 pp. QC880.4.T5T76 2007
  • *Wallace, J. M., and P. V. Hobbs, 2006: Atmospheric Science.  An Introductory Survey. Second Edition.  New York, Academic Press, 483 pp.  Chapter 3 QC861.3.W35 2006 
  • Zdunkowski, W. and A. Bott, 2004: Thermodynamics of the Atmosphere. Cambridge University Press, 251 pp. QC880.4.T5Z38 2004
  • It is strongly recommended that you own a calculus-based physics text, Bohren and Albrecht, and Wallace and Hobbs as well as your calculus textbooks.                    

*  On reserve at the EMS Library


“We must attribute to heat the great movements that we observe all about us on the Earth. Heat is the cause of currents in the atmosphere, of the rising motion of clouds, of the falling of rain and of other atmospheric phenomena . . .”             - Sadi Carnot (1824) 


“A theory is more impressive the greater is the simplicity of its premises, the more different are the things it relates, and the more extended its range of applicability. Therefore, the deep impression which classical thermodynamics made on me. It is the only physical theory of universal content which I am convinced, that within the framework of applicability of its basic concepts, will never be overthrown."

- Albert Einstein


As a student majoring in Meteorology, you are expected to have a reasonable background in mathematics (through differential equations) and physics (mechanics, electricity and magnetism) before studying thermodynamics.  Students with weak backgrounds in these fundamental disciplines are advised to postpone enrollment in this course.  

Each student is expected to keep up with the subject matter and to participate actively and effectively in class.  Participation may take the form of responding to questions posed by the instructor or of asking content-related questions in or out of the classroom.  Exams serve to test not only your general knowledge of the subject matter, but also your ability to apply that knowledge to solving new problems. 

Homework, assigned approximately weekly, must be turned in on time.  Outside assignments may be challenging, but they nevertheless constitute only one way to learn.  Reading from the required text and from the several books put on reserve in the EMS library is essential.  Experience also suggests that rewriting your class notes within a day or so of each lecture leads to significantly enhanced learning of complex material.  Remember that what you get out of any endeavor is proportionate to the effort you put into it.  You are here to learn, not to get a grade. 

Reminder about academic integrity:  Cheating and plagiarism are serious offenses that may be grounds for failing an assignment, an exam, or even the course.  Collaboration with classmates can be an effective way of learning, especially when you are the one teaching others.  In any case, the final work must be your own, a clear expression of your level of understanding.  Please review the College policies related to academic integrity on the web at

Objectives and Outcomes for Meteo 431

Objectives for Meteo 431:

  1. Students can demonstrate an ability to apply thermodynamic principles quantitatively to atmospheric problems (see program objectives 1 and 3 below).
  2. Students can demonstrate the use of thermodynamics equations in determining the thermal structure of basic atmospheric phenomena (see program objectives 2 below). 

Outcomes for Meteo 431:

  1. Students can demonstrate knowledge of how thermal energy and the first law of thermodynamics is applied to describe atmospheric thermal properties and structure (see program outcomes b below).
  2. Students can demonstrate knowledge of how entropy and the second law of thermodynamics are applied to basic thermal problems (see program outcome b below).
  3. Students can demonstrate knowledge of the process of phase change in atmospheric phenomena (see program outcomes b and c below).
  4. Students can demonstrate an ability to analyze atmospheric soundings using a thermodynamic diagram (see program outcomes a, b, c, and d below). 

Program Objectives

  1. To produce graduates who possess quantitative, scientific reasoning skills that can be applied to atmospheric problems.
  2. To produce graduates who have a general knowledge of a range of atmospheric phenomena and applications, and have expertise in one or more program subdisciplines or related interdisciplinary areas.
  3. To produce graduates who are equipped to contribute to solving problems in the atmospheric sciences and related disciplines, through service in business or as educators, researchers, and leaders in academia, government, the private sector, and civil society.

Program Outcomes

  1. Graduates can demonstrate skills for interpreting and applying atmospheric observations.
  2. Graduates can demonstrate knowledge of the atmosphere and its evolution.
  3. Graduates can demonstrate knowledge of the role of water in the atmosphere.
  4. Graduates can demonstrate facility with computer applications to atmospheric problems.
  5. Graduates can demonstrate skills for communicating their technical knowledge.



Students who do not meet these prerequisites after being informed in writing by the instructor may be dis-enrolled during the first 10-day free add-drop period: http:/ If you have not completed the listed prerequisites, then promptly consult with the instructor if you have not done so already. Students who re-enroll after being dis-enrolled according to this policy are in violation of Item 15 on the Student Code of Conduct:

Assistance with Textbooks

Penn State honors and values the socioeconomic diversity of our students. If you require assistance with the costs of textbooks for this course, contact the Office of Student and Family Services (120 Boucke Building, 863-4926, For additional need related to socioeconomic status please visit

Academic Integrity

Students in this class are expected to write up their problem sets individually, to work the exams on their own, and to write their papers in their own words using proper citations.  Class members may work on the problem sets in groups, but then each student must write up the answers separately.  Students are not to copy problem or exam answers from another person's paper and present them as their own; students may not plagiarize text from papers or websites written by others.  Students who present other people's work as their own will receive at least a 0 on the assignment and may well receive an F or XF in the course.  Please see: Earth and Mineral Sciences Academic Integrity Policy:, which this course adopts.

Course Copyright

All course materials students receive or to which students have online access are protected by copyright laws. Students may use course materials and make copies for their own use as needed, but unauthorized distribution and/or uploading of materials without the instructor’s express permission is strictly prohibited. University Policy AD 40, the University Policy Recording of Classroom Activities and Note Taking Services addresses this issue. Students who engage in the unauthorized distribution of copyrighted materials may be held in violation of the University’s Code of Conduct, and/or liable under Federal and State laws.

Accommodations for Students with Disabilities

Penn State welcomes students with disabilities into the University's educational programs. Every Penn State campus has an office for students with disabilities. The Office for Disability Services (ODS) website provides contact information for every Penn State campus: ( For further information, please visit the Office for Disability Services website (

In order to receive consideration for reasonable accommodations, you must contact the appropriate disability services office at the campus where you are officially enrolled, participate in an intake interview, and provide documentation based on the documentation guidelines ( If the documentation supports your request for reasonable accommodations, your campus’s disability services office will provide you with an accommodation letter. Please share this letter with your instructors and discuss the accommodations with them as early in your courses as possible. You must follow this process for every semester that you request accommodations. 


This course abides by the Penn State Class Attendance Policy 42-27:, Attendance Policy E-11:, and Conflict Exam Policy 44-35: Please also see Illness Verification Policy:, and Religious Observance Policy: Students who miss class for legitimate reasons will be given a reasonable opportunity to make up missed work, including exams and quizzes.  Students are not required to secure the signature of medical personnel in the case of illness or injury and should use their best judgment on whether they are well enough to attend class or not; the University Health Center will not provide medical verification for minor illnesses or injuries. Other legitimate reasons for missing class include religious observance, family emergencies, and regularly scheduled university-approved curricular or extracurricular activities.  Students who encounter serious family, health, or personal situations that result in extended absences should contact the Office of Student and Family Services for help:  Whenever possible, students participating in University-approved activities should submit to the instructor a Class Absence Form available from the Registrar's Office:, at least one week prior to the activity.

Weather Delays

Campus emergencies, including weather delays, are announced on Penn State News: http:/ and communicated to cellphones, email, the Penn State Facebook page, and Twitter via PSUAlert (Sign up at:

Penn State E-mail Accounts

All official communications from Penn State are sent to students' Penn State e-mail accounts. Be sure to check your Penn State account regularly, or forward your Penn State e-mail to your preferred e-mail account, so you don't miss any important information.

Deferred Grades

If you are prevented from completing this course within the prescribed amount of time, it is possible to have the grade deferred with the concurrence of the instructor. To seek a deferred grade, you must submit a written request (by e-mail or U.S. post) to your instructor describing the reason(s) for the request. It is up to your instructor to determine whether or not you will be permitted to receive a deferred grade. If, for any reason, the course work for the deferred grade is not complete by the assigned time, a grade of "F" will be automatically entered on your transcript. 

Military Personnel

Veterans and currently serving military personnel and/or spouses with unique circumstances (e.g., upcoming deployments, drill/duty requirements, disabilities, VA appointments, etc.) are welcome and encouraged to communicate these, in advance if possible, to the instructor in the case that special arrangements need to be made.

Technical Requirements

For this course, we recommend the minimum technical requirements outlined on the Dutton Institute Technical Requirements page (, including the requirements listed for same-time, synchronous communications. If you need technical assistance at any point during the course, please contact the ITS Help Desk ( 


The term "Netiquette" refers to the etiquette guidelines for electronic communications, such as e-mail and bulletin board postings. Netiquette covers not only rules to maintain civility in discussions, but also special guidelines unique to the electronic nature of forum messages. Please review Virginia Shea's "The Core Rules of Netiquette" ( for general guidelines that should be followed when communicating in this course. 

Disclaimer Statement

Please note that the specifics of this Course Syllabus can be changed at any time, and you will be responsible for abiding by any such changes. Changes will be posted to the course discussion forum.

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