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Author: Joseph M. Powers

"When you measure what you are speaking about and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge about it is of a meagre and unsatisfactory kind."

-- William Thomson (Lord Kelvin), 1824-1907


"Die Energie der Welt ist konstant. Die Entropie der Welt strebt einem Maximum zu."

Course Description

The course will consider the fundamental science of classical thermodynamics and its practical applications. Problem solving will be emphasized, including problem formulation, analytic, and computational solutions. Topics include:

  • Some introductory comments: some definitions, some history, some philosophy, relevance of thermodynamics to engineering applications,
  • Concepts: property, state, system, process, temperature, pressure, density, volume, energy, units, zeroth law of thermodynamics,
  • Properties of a pure substance: vapor/liquid/solid phase equilibrium, independent properties, thermal equation of state, tables of properties, ideal gas limit, some non-ideal state equations, interpolation,
  • Work and heat: some mathematics, simple compressible systems, work, heat,
  • The first law of thermodynamics: classical formulation of the first law, internal, kinetic, and potential energy, enthalpy, constant pressure and constant volume specific heats, tables of energy and enthalpy, constant and temperature-dependent specific heats for ideal gases, time-dependency,
  • First law analysis for a control volume: detailed derivations, control volume mass conservation, first law formulation for control volume, steady-state processes, transient processes, devices, introduction to the Rankine cycle,
  • The second law of thermodynamics: statements of the second law, heat engines and refrigerators, reversible processes, absolute temperature scale, Carnot cycles
  • Entropy: theoretical development, second law in terms of entropy, the Gibbs equation, entropy for ideal gases, entropy change for reversible and irreversible processes, tabulation of entropy, adiabatic reversible processes for ideal gases, entorpy of mixing, probabilistic approach,
  • Second law analysis for a control volumes: irreversible entropy production, Bernoulli’s principle, steady state and transient formulation, efficiency of components,
  • Cycles: Rankine, Brayton, refrigeration, and
  • Mathematical foundations: Maxwell relations, Legendre transformations, heat capacity, real gas behavior and non-ideal equations of state, adiabatic sound speed, introduction to compressible flow.

Course Objectives

  • Learn the scientific principles underlying classical thermodynamics: energy conservation, the entropy inequality, and equations of state.
  • Learn how to apply the principles of thermodynamics to systems of practical engineering importance such as power plants, internal combustion engines, and refrigeration devices.
  • Gain an enhanced appreciation for the importance of careful verified calculation for use in engineering devices in which life and treasure are at risk.
  • Become familiar with aspects of the intellectual history of thermodynamics.
  • Gain some skills in technical writing and modern engineering software tools.



  • MATH 20550-Calculus III


  • AME 20221-Mechanics I

Required Textbooks

  • C. Borgnakke and R. E. Sonntag, 2009, Fundamentals of Thermodynamics, Seventh Edition, John Wiley.
  • H. C. von Baeyer, 1998, Warmth Disperses and Time Passes: The History of Heat, Modern Library.

Course Notes

Required Work

  • Exams will be open book, closed notes and held in class. The final exam will be comprehensive. You can bring one 8 1/2” by 11” sheet with notes on both sides to the first exam, two to the second, and three to the final.
  • Homework will be assigned weekly, and generally due at the beginning of class on Friday. All homework will be graded and returned. Graded homework will be available in the public space near the elevator on the third floor of Fitzpatrick Hall. Homework must be done on one side only of 8 1/2” by 11” engineering paper with no frayed edges. Multiple pages must be stapled. You should briefly restate the problem, give a sketch if helpful, give all necessary analysis, and place a box around your final answer. All plots must be computer generated, trimmed, and taped to engineering paper. Label all axes. Raw Mathematica or Maple output will not be graded. Neatness and effective communication are considered in grading as well as the final answer itself.
  • Short closed book, closed notes quizzes will be given on a regular basis. Generally these will be on Friday, but they may be given without prior announcement at the instructor’s discretion.
  • Two short (one page maximum) critical reviews of works from the literature will be required. The first will be a review of the von Baeyer book. The second review must consider an article on thermodynamics from the technical journal Nature and consider some aspect of thermodynamics related to energy. Detailed technical articles should be studied, not news summaries. The reviews are required to be written in a LaTeX format and will be checked primarily for style, format, grammar, and content.
  • I will make arrangements for a tour of the Notre Dame power plant. Attendance will be required.
  • Attendance in class is expected. A formal roll will not be taken unless the instructor feels it necessary. At the instructor’s discretion, a failing grade may be given for excessive absences; this step will only be taken following a written warning to the student.
  • An Office of Student Affairs-approved written excuse will be required in order for any consideration to be given for any required work (for example, examinations, quizzes, or homework) which is not completed at the expected time. The instructor reserves the right to require all work to be completed to receive a passing grade.


Grades will be assigned based on students’ performance on examinations, quizzes, homework, and papers.

Component Percentage
Exam I 15%
Exam II 15%
Quizzes 15%
Homework 13%
Final Examination 40%
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