16.050 | Fall 2002 | Undergraduate

Thermal Energy


Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

Recitations: 1 session / week, 1 hour / session

The typical student enrolled in 16.050 is a junior in the Department of Aeronautics and Astronautics at MIT. The student will have completed Unified Engineering while a sophomore. Unified Engineering (16.01-16.04) presents, among other disciplines, first courses in thermodynamics and propulsion.

Subject Information

Concepts Addressed in 16.050

Energy exchange in propulsion and power processes; the second law of thermodynamics; reversible and irreversible processes; quantification of irreversibility and connection to lost work; application of the first and second laws to engineering systems (propulsion cycles, gas and vapor power cycles, reacting flows); rates of energy transfer and heat exchange in aerospace devices.

Learning Objectives

Be able to:

  1. Use the Second Law of Thermodynamics to evaluate the limitations on thermal-mechanical energy conversion in aerospace power and propulsion systems;
  2. Estimate heat transfer rates in simple engineering situations such as a convectively cooled turbine blade;
  3. Carry out conceptual design of basic aerothermal components and systems.

Measurable Outcomes [Assessment Method]

Be able to:

  1. Explain the physical content and implications of the second law in non-mathematical terms [concept quiz, quiz];
  2. Define entropy [concept quiz, homework];
  3. Estimate the thermodynamic efficiency and power production of an arbitrary ideal cycle [concept quiz, homework, quiz];
  4. Obtain a basic physical intuition for the thermodynamic performance of real power and propulsion devices as indicated by recognition of what good, average, and poor performance is (metrics and numbers) for engineering power and propulsion devices [concept quiz, homework];
  5. Use entropy calculations as a tool for evaluating irreversibility (lost work) in engineering processes [homework, quiz];
  6. Estimate the effect of losses on thermodynamic efficiency [homework, quiz];
  7. Estimate heat transfer rates for aerospace vehicle conditions [homework, quiz];
  8. Carry out a thermodynamic analysis of a basic (real or proposed) power or propulsion producer, assess performance, and suggest where design improvements would be most effective [GE design project].

Outline of Lectures †

**Part 0 (Prelude): Introduction and Review of Unified Engineering Thermodynamics (3 lectures)
**[IAW pp. 2-22, 32-41 (see IAW for detailed SB & VW references); VN Chapter 1]

Self-assessment on thermodynamic concepts and applications
Thermodynamic systems
Thermodynamic properties and states
Energy, work and heat
The first law of thermodynamics
Enthalpy, a useful property
Relation between systems and control volumes; adaptation of system formulation to a fixed control volume, application to fluid processes
The first law for a control volume (steady flow energy equation)

Part 1: The Second Law of Thermodynamics (10 lectures)

1.A. Background to the Second Law of Thermodynamics (3 lectures)
[IAW 23-31 (see IAW for detailed SB & VW references); VN Chapters 2, 3, 4]

Some properties of engineering cycles; work and efficiency
Carnot cycles
The Brayton cycle (jet propulsion cycle)
Gas turbine technology and thermodynamics
Refrigerators and heat pumps; Carnot cycles in reverse
Reversibility and irreversibility in natural processes
Difference between free expansion of a gas and reversible isothermal expansion
Features of reversible processes

1.B. The Second Law of Thermodynamics (3 lectures)
[IAW 42-50; VN Chapter 5; SB & VW-6.3, 6.4, Chapter 7]

Concept and statements of the second law (Why do we need a second law?)
Axiomatic statements of the laws of thermodynamics
Combined first and second law expressions
Entropy changes in an ideal gas
Calculation of entropy change in some basic processes

1.C. Applications of the Second Law (4 lectures)
[VN-Chapter 6; SB & VW-8.1, 8.2, 8.5, 8.6, 8.7, 8.8, 9.6]

Limitations on the work that can be supplied by a heat engine
The thermodynamic temperature scale
Representation of processes in T-s coordinates
Brayton cycle in T-s coordinates
Irreversibility, entropy changes, and “lost work”
Entropy and “unavailable energy” (lost work by another name)
Examples of lost work in engineering processes
Interpretation of entropy from a microscopic perspective: entropy and randomness
Recap: How do we answer the question “What is entropy?”

Part 2. Applications of Thermodynamics to Engineering Systems (13 lectures)

2.A. Gas Power and Propulsion Cycles (6 lectures)
[SB & VW-11.8, 11.9, 11.11, 11.12, 11.13, 11.14, 11.15]

The internal combustion engine (Otto cycle)
Diesel cycle
Brayton cycle
Brayton cycle for jet propulsion; the ideal ramjet
The Breguet range equation
Performance of the ideal ramjet
Effect of departures from ideal behavior-real cycles

2.B. Power Cycles with Two-Phase Media (Vapor Power Cycles) (4 Lectures)
[SB & VW-Chapter 3, 11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7]

Behavior of two-phase systems
Work and heat transfer with two-phase media
The Carnot cycle as a two-phase power cycle
Rankine power cycles
Enhancement of, and effect of design parameters on, Rankine cycles
Combined cycles in stationary gas turbines for power production

2.C. Introduction to Thermochemistry (3 lectures)
[SB & VW-14.1-14.6]

Fuel-air ratio
Enthalpy of formation
First law analysis of reacting systems
Adiabatic flame temperature

Part 3: Fundamentals of Heat Transfer (11 lectures)

3.A. Introduction to Conduction Heat Transfer (3 lectures)
[HT-1.0, 2.0 to 2.3]

1.0 Modes of heat transfer (conduction, convection and radiation)

2.0 Conduction heat transfer
Steady-state one-dimensional conduction
Thermal resistance circuits
Steady quasi-one dimensional heat flow

3.B. Introduction to Convection Heat Transfer (3 Lectures)
[HT-3.0 to 3.3, 4.0, 5.0, 6.0, 7.0]

3.0 Convective heat transfer
The Reynolds’ analogy
Combined conduction and convection
Dimensionless numbers and analysis of results

4.0 Temperature distributions in the presence of heat sources

5.0 Heat transfer from a fin

6.0 Transient heat transfer (convective cooling or heating)

7.0 Some considerations in modeling complex physical processes

3.C. Applications of the Concepts: Heat Exchangers (2 Lectures)
[HT-8.0, 8.1]

8.0 Heat exchangers
Efficiency of a counterflow heat exchanger

3.D. Introduction to Thermal Radiation and Radiation Heat Transfer (3 lectures)
[HT-9.0 to 9.4]

9.0 Radiation heat transfer (heat transfer by thermal radiation)
Ideal radiators
Kirchoff’s laws and “real bodies”
Radiation heat transfer between planar surfaces
Radiation heat transfer between black surfaces of arbitrary geometry

† Lecture divisions correspond to sections in 16.050 notes.
Relevant references given in brackets [ ]

Professor Zoltan Spakovszky


  1. Thermal Energy (16.050) Class Notes - Fall 2002.
  2. Understanding Thermodynamics, by Van Ness, H. C., Dover Press Publishers (referred to in the lecture outline as VN).

Other Reference Material

  1. Thermodynamics Notes for Unified Engineering, compiled by Professor Waitz (referred to in the lecture outline as IAW).
  2. Handouts on specific topics as warranted.
  3. Fundamentals of Thermodynamics, Sonntag, R. E., Borgnakke, C, and Van Wylen, G. J., John Wiley Publishers, 1998 (referred to in lecture outline as SB & VW).

GE Design Project

A design project related to gas turbine engines will be conducted with GE Aircraft Engines. Teams of 4 to 5 students will be formed and the workload will be equivalent to about two problem sets. The deliverables are a written report and the presentation of the work to a GE review committee. The best two teams will be awarded a prize and the GE project will count as two problem sets.

Homework, Quizzes, and Final Exam

There will be two quizzes during the term plus a final exam. The homework (including reading assignments plus the GE design project) will count 35%, the quizzes will count 15% each, and the final exam will count 30%. The instructor reserves the right to alter the percentages slightly, depending on circumstances.

Each week, the 12 course hours are intended to be distributed approximately as follows:
3 hours of lecture, 1 hour of recitation, 2-3 hours of reading and reviewing notes, 5-6 hours of homework.

Homework assignments will be due at the beginning of class. Any unexcused late assignments will receive zero credit.

The remaining 5% of the grade will be based on student performance in various exercises (many of which will occur in class). These may include answering questions in class, either verbally or using the PRS system, submitting assessment surveys, or taking concept quizzes. In all cases the lowest 20% of the scores can be dropped to provide some flexibility for missed classes, etc. There will be no make-up opportunities granted for missing these activities.

[Note: A student’s performance on quizzes is an assessment of individual performance (versus that of a study group, for example). Therefore if an individual’s performance on the quizzes is significantly lower than on the homework, the average quiz grade may be given proportionally greater weight than described above.]

The basis for grading in the course is as described in the Rules of the MIT Faculty. The description of grades is given below under Basis for Grades.

Class Exercises

The lectures are thrice a week. Each session is for one hour. These are the primary presentation of the subject material by the instructor.

There is a recitation once a week for one hour. The recitations will be given by (at different times) the graduate TA and the undergraduate TAs. The recitations review the material from previous lectures and introduce relevant examples, which may be related to the assigned homework.

As in Unified, attendance at lectures and recitations is considered mandatory. Although no formal roll call will be taken, participation during in-class exercises will represent part of your grade.

Quiz Help Sessions

It is planned there will be help sessions given by the instructor prior to each quiz and to the final.

PRS System

Each student will be distributed a remote transmitter to be used with the Personal Response System (PRS). Each one has its own number and is assigned to a particular student. Students are responsible for bringing their transmitter to every lecture, in order to participate in exercises that use PRS. Since class participation will be, in part, gauged by each student’s responses, operating other student’s transmitters in their place will be considered a violation of MIT’s academic honesty policy.

The transmitters cost approximately $50. If a transmitter is lost the student will be responsible for paying for a replacement.

Policy on Collaboration and Cheating

The policy on collaboration and cheating will be the same as that specified in Unified Engineering. The policy on Academic Honesty and Study Group Guidelines are given below.

Academic Honesty

The fundamental principle of academic integrity is that you must fairly represent the authorship of the intellectual content of the work you submit for credit. In the context of this class, this means that if you consult with others (such as fellow students, TA’s, faculty) in the process of completing homework, you must acknowledge their contribution in any way that reflects their true ownership of the ideas and methods you borrowed.

Discussion among students to understand the homework problems or to prepare for laboratories or quizzes is encouraged. COLLABORATION ON HOMEWORK IS ALLOWED AS LONG AS ALL REFERENCES (BOTH LITERATURE AND PEOPLE) USED ARE NAMED CLEARLY AT THE END OF THE ASSIGNMENT. Word-by-word copies of someone else’s solution or parts of a solution handed in for credit will be considered cheating unless there is a reference to the source for any part of the work which was copied verbatim. FAILURE TO CITE OTHER STUDENT’S CONTRIBUTION TO YOUR HOMEWORK SOLUTION WILL BE CONSIDERED CHEATING. The official Institute policy regarding academic honesty can be found in the MIT Bulletin Course and Degrees Issue under “Academic Procedures and Institute Regulations.”

MIT’s academic honesty policy can be found at the following link: https://policies-procedures.mit.edu/academic-misconduct-and-dishonesty/

Study Group Guidelines

Study groups are considered an educationally beneficial activity. However, at the end of each problem on which you collaborated with another student you must cite the students and the interaction. The purpose of this is to acknowledge their contribution to your work. Some examples follow:

  1. You discuss concepts, approaches and methods that could be applied to a homework problem before either of you start your written solution. This process is encouraged. You are not required to make a written acknowledgment of this type of interaction.
  2. After working on a problem independently, you compare answers with another student, which confirms your solution. You should acknowledge that the other student’s solution was used to check your own. No credit will be lost if the solutions are correct and the acknowledgments is made.
  3. After working on a problem independently, you compare answers with another student, which alerts you to an error in your own work. You should state at the end of the problem that you corrected your error on the basis of checking answers with the other student. No credit will be lost if the solution is correct and the acknowledgment is made, and no direct copying of the correct solution is involved.
  4. You and another student work through a problem together exchanging ideas as the solution progresses. Each of you should state at the end of the problem that you worked jointly. No credit will be lost if the solutions are correct and the acknowledgment is made.
  5. You copy all or part of a solution from a reference such as a textbook or a “bible.” You should cite the reference. Partial credit will be given, since there is some educational value in reading and understanding the solution. However, this practice is strongly discouraged, and should be used only when you are unable to solve the problem without assistance.
  6. You copy verbatim all or part of a solution from another student. This process is prohibited. You will receive no credit for verbatim copying from another student when you have not made any intellectual contribution to the work you are both submitting for credit.

Basis for Grades

The rules of the MIT faculty define grades in terms of the degree of the mastery of course material:

A Exceptionally good performance, demonstrating a superior understanding of the subject matter, a foundation of extensive knowledge, and a skillful use of concepts and/or materials.

B Good performance, demonstrating capacity to use the appropriate concepts, a good understanding of the subject matter, and an ability to handle the problems and materials encountered in the subject.

C Adequate performance, demonstrating an adequate understanding of the subject matter, an ability to handle relatively simple problems, and adequate preparation for moving on to more advanced work in the field.

D Minimally acceptable performance, demonstrating at least partial familiarity with the subject matter and some capacity to deal with relatively simple problems, but also demonstrating deficiencies serious enough to make it inadvisable to proceed further in the field without additional work.

Course Info

As Taught In
Fall 2002
Learning Resource Types
Problem Sets
Lecture Notes