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Teaching Engineering Thermodynamics to Undergraduate Students

Zhigang Suo's picture

I have just volunteered to teach engineering thermodynamics to undergraduates in the Fall semester of 2011.  The students will be from all fields of engineering, primarily mechanical engineering, environmental engineering, and bioengineering.  I have never taught this course before, and would love to hear from you about your experience, either as a student or as a teacher. 

Here is what I have found from the website about the course.

Engineering Science 181 Engineering Thermodynamics

Introduction to engineering thermodynamics with emphasis on classical thermodynamics. Topics:

  • Zeroth law and temperature
  • Properties of single-component gases, liquids, and solids
  • steam tables
  • Equations of state for ideal and simple nonideal substances
  • First law, heat and heat transfer, work, internal energy, enthalpy
  • Second law, entropy, free energy
  • Third law
  • Heat engines and important engineering applications such as refrigerators, power cycles
  • Properties and simple models of solutions
  • Phase and chemical equilibrium in multicomponent systems; chemical potential
  • Laboratory included


  • Physics 11 or 15
  • Applied Mathematics or Mathematics 21
  • chemistry at the level of a good secondary school course or Chemistry 5

Mike Aziz has been teaching the course, and has used the following textbook:

Borgnakke and Sunntag, Fundamentals of Thermodynamics 

Please let me know your thoughts about the course.  What textbook do you recommend?  What do you find effective for learning thermodynamics for the first time?  What are useful online resources?  Any innovation in teaching the subject in connection with environment and energy? 


Cengel Boles is a a spectacular book. See The book makes the subject very, very interesting.

Zhigang Suo's picture

Dear Amit:  Thank you very much for the suggestion.  Over the weekend I spent some time looking at books on Amazon.  Quite a few interesting books turned up under the word Thermodynamics.  The text by Cengel and Boles is high on the list, and is well reviewed by the readers.  Thank you very much for your suggestion.  I'll check this book out.    

Pradeep Sharma's picture

Zhigang, I am teaching a graduate course in thermodynamics and statistical mechanics in the Spring (---I also volunteered to teach this). I have never taught undergraduate thermodynamics and to be honest find the current flavor of "engineering" thermodynamics not much to my taste. I think you are already aware of the book by Dill and Bromberg...I would prefer this book supplemented with the requisite engineering topics. My personal opinion is that statistical mechanics should be introduced at the outset even in elementary courses in thermodynamics (--an opinion that I am afraid is not widely shared). There is one book (written by a fellow mechanician) which is very interesting and parts of it may be used in both undergraduate and graduate courses:

The emphasis of this book is on solids. Even though Professor Ericksen used his book for an undergraduate course and the mathematical pre-requisites are indeed quite elementary, the book does demand some maturity.


Amit: I will check out the book you recommended.

Zhigang Suo's picture

Dear Pradeep:  I would love to hear your experience in teaching Thermodynamics to graduate students.  Indeed I enjoyed Molecular Driving Forces by Dill and Bromberg.  One of the authors, Ken Dill, is an active researcher; I have also read some of his papers.  Over the weekend I learned on Amazon that a new edition of the book has just come out in December 2010.  The text has a subtitle:  Statistical Thermodynamics in Biology, Chemistry, and Nanoscience.  The book, however, does not say much about engineering applications of Thermodyanmics (power plants, refrigerators, feul cells, etc.).

I also really like the book by Ericksen.  This book might be particularly good for a graduate course on solid mechanics.  It describes some interesting applications of thermodyanmics to solid mechanics, but does not develop thermodynamics from scratch.  I have just noticed that much of the content of the book is posted on Amazon.

I'll give the matter more thoughts and think it over what I really want to cover in my undergarduate course on Engineering Thermodynamics.  I'll come back to you for more feedback.  

Pradeep Sharma's picture

Zhigang, I forgot to add in my post.....there is a new edition that just came out for Bromberg and Dill's book. The authors added new chapters to the book including thermodynamics for nanosystems.

Personally (and this is strictly a personal opinion as a "student"), I find teaching of some of the engineering elements of thermodynamics such as steam tables, application to engines etc somewhat un-interesting. Perhaps for this reason, I did not warm up to thermodynamics for a long time and only after becoming an independent researcher I fell in love with this subject and began to marvel at its nearly universal applicability. For this very reason, I favor teaching thermodynamics as a "science" subject with application to various areas (----despite some shortcoming, Dill/Bromberg appear to do this). The course I took as an undergraduate was very heavy on the engineering aspects......Mixing statistical mechanics at the outset also emphasizes (as well put by Sethna) that statistical thermodynamics can be used all the way from cards in casinos to black holes---something that was almost completely missing from my undergraduate courses.

Dear Zhigang,

Here are a few suggestions:

1. Do introduce Stat. Mech. right in an introductory course too. [Pradeep, I have always had this opinion---at least since I ran into Huang's text ~20 years ago anyway!] The treatment may not be mathematically in-depth, of course. However, the topic still should be included so that the student develops an appreciation for the particle model---the simplicity it leads to. And, historically, the two subjects anyway got developed almost simultaneously even though all the initial formulations, of course, were in the thermodynamic (i.e. continuum) terms.

2. De-emphasize the deductive drudgery of Maxwell's relations, otherwise a perennial favorite of teachers. The topic should be covered, no doubt. However, deductive manipulations should not be emphasized in any work that counts towards grades. (Else, in trying to master those relations, including via memorizing those relations, the student is actually led away from both the theoretical beauty and the grandeur of thermodynamics itself). Oh, BTW, also tell them a bit about the linearity assumption---the limitations of those relations.

3. Include something on electrochemical topics. Thermodynamics of batteries, of fuel cells... Here I am trying hard to recall a discovery concerning batteries (or so) that was basically made by applying the mathematical relations of thermodynamics. Somehow I fail to recall it right now... May be I will come back and add.

4. As Pradeep suggests, something towards thermodynamics of solids may be included. But not in detail. May be half a lecture (30 minutes) or so, at the most. I am not sure if the student would be ready for any more on this topic in the very first course on thermodynamics. ... Indeed, the student might not have taken anything on solid mechanics at all, by this time.

5. Do introduce the topic of the systems away from equilibrium. For systems near equilibrium, a little bit of mathematics (for may be just one model/situation) may be introduced. The mathematics should be just enough that the student develops an appreciation for what is involved. Then, also give them some flavor of the theoretical approaches developed to address systems farther away from equilibrium. I think at least a conceptual treatment should be easily possible.


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Zhigang Suo's picture

Dear Ajit:  Thank you so much for your great suggestions.  Here are my notes
stimulated by your suggestions.  I’ll use your numbers.

  1. Introduce Statistical Mechanics.  I agree with you and Pradeep.  I plan to tell the students what is entropy in Lecture 1, and how to measure entropy in Lecture 2.  I have written notes on these two lectures, and have used them in a graduate course on advanced elasticity.  I’ll think it over how to do it in this undergraduate class.
  2. De-emphasize Maxwell Relations.  Indeed, thermodynamics should not be an exercise of partial differentiation.  I’m thinking of introducing Gibbs’s graphical approach to the thermodynamic surface, along with the analytical approach.  What I have in mind is described in Section II of the paper on the Theory of Dielectric Elastomers.  But I’ll be careful.  As you pointed out, these mathematical ideas may distract students.
  3. Include electrochemical topics.  I plan to describe several phenomena and devices in sufficient detail to make them “real”  to the students.  In addition to thermomechanical energy conversion, I’ll include electrochemical and electromechanical energy conversion.
  4. Include some thermodynamics of solids.  I’m thinking of including some description of thermoelasticity.  Perhaps I can describe to students how rubber elasticity works.
  5. Introduce systems away from equilibrium.  Do you have mass and heat transport in mind?  This is an excellent idea.  I’ll think how it might be implemented in this class.

I hope to draft a plan of lectures over the holidays, and come back to get feedback from you all.

Dear Zhigang,

Yes, I was aware of your excellent notes on statistical mechanics. ... I do recall your excellent expressions (the excellent formulations, in words) in your notes about the fundamental ideas concerning temperature, though I think the approach therein is suitable only for graduate students---historically, the appreciation for the Zeroth law came long before the quantum ideas were even nascent.... Anyway, as you yourself note above, a bit of thought will have to go into the question of how to make it accessible to the undergraduates.

Regarding systems away from equilibrium... Ummm... I really didn't think a lot about it when I mentioned this point above! ... As I was going through the syllabus points, I noticed the absence of non-equilibrium thermodynamics, and immediately recollected an excellent popular science kind of book by Ilya Prigogine (with Isabelle Stenger) that I had read sometime in mid/late-1980s. I think the title was "Order Out of Chaos." In that book, I now only faintly recollect, Prigogine had first touched upon Onsager's reciprocity relations, and then had also gone on to describe more advanced work, in a fairly accessible (popular science-like) manner. I had said to myself, right then, how much more interesting our early undergraduate courses on thermodynamics would have been if we could have been exposed to such lines of thought too. .... It was purely based on this recollection that I thought of suggesting a coverage of non-equilibrium thermodynamics.

Speaking personally, I have done 4 courses on thermodynamics, suffering at least in part through each of them: (i) first-year UG: introductory, (ii) second-year UG: metallurgical thermodynamics and kinetics, (iii) second-year UG: as a major part of a course on mechanical engg. for metallurgical UGs, and (iv) a graduate materials course in thermodynamics of solids (Swalin). Not a single one had statistical mechanics in it; I supplied my understanding through recall of high-school physics and then also going through Huang's text. Not a single one had non-equilibrium thermodynamics---neither the nonlinearities in heat and mass transport nor the dissipative structures and the Bernard cells. ... People get taught isentropic flow in CFD, but can't connect it to their knowledge of thermodynamics...

Now, I am well aware that, today, after having gone through 4 courses in a distant past, it is easy to mix things up and believe that even the very first course could address all these things. It is always easy to mix things up as you grow older. Yet, at the same time, one likes to ponder: Isn't at least a conceptual treatment for such topics possible? Shouldn't the undergraduates be told about the broadest scope first, right via their formal courses? Personally, I think that's the way it should be done. 

Actually, I haven't had a formal or informal work to do with thermodynamics per say, for the past 15+ years or so. As such, I can't tell what books will be good and all. But, today, after a bit of Google search, I found a couple of books which I haven't read but which I think could be very relevant: Dilip Kondepudi and Ilya Prigogine's "Modern Thermodynamics: From Heat Engines to Dissipative Structures" [^], and Kondepudi's more recent offshoot from it: "Introduction to Modern Thermodynamics" [^]. If other iMechanicians have read or used these books, they may be able to tell if these books are suitable for a very first undergraduate course.

See how it all might be brought together.... I now look forward to reading your class-notes.


PS: This reply is already too long, but can't resist one more bit! If a student or group of them is particularly inclined towards programming, then you might ask them to build a small software applet that takes in variables like P, V, T, S, H, A, etc. as input, and shows the relevant Maxwell's identities and other relationships as output. The topic is that "mechanical"!

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Amit Acharya's picture


For u/g teaching about heat engines etc. you may wish to check out Truesdell and Bharatha's book

The concepts and logic of classical thermodynamics as a theory of
heat engines, rigorously constructed upon the foundation laid by S.
Carnot and F. Reech

and form your own opinion. I don't care so much about the claims of 'rigor' etc. but when I had looked through it (a long time ago), it did present the material in an unambiguous way. The mathematics is just differential calculus.


- Amit


Zhigang Suo's picture

Dear Amit:  Thank you for the suggestion.  I heard of the book, but have never seen it myself.  The price on Amazon is steep:  $50 for a used copy of a book of 154 pages!  Harvard library does not have a copy, but I have just requested the book from the inter-library loan. 

Your mentioning of Truesdell reminds me of a quote.  I'm half way through a biography of Lord Kelvin.  Here is what Load Kelvin said of his friend Tait:

"We never agreed to differ, always fought it out.  But it was almost as great a pleasure to fight Tait as to agree with him."



I was asked to teach thermodynamics in F08 and S09 just upon joining UMaine as an assistant professor. I've taught many other courses ever since but I must say teaching thermo was a different experience. I used the same book as you mentioned, Borgnakke and Sunntag's "Fundamentals of Thermodynamics". The book is good, just a few typos here and there and lots of HW problems at the end of each section, ranging from easy to difficult. I found the section about "Heat" in Chapter 4 (where the book introduces the heat transfer) rather weak. This concept should have been better described, I guess, as a good grasp of heat transfer later will help to understand the reversibility in a process much easier.

Things would go fairly smoothly till just after the 1st law, concepts are all easy to understand and perhaps intuitive for many students. BUT, the problem starts when you want to talk about "entropy" and of course teach the 2nd law. The book does not help, and that's not the problem of this particular book, I checked many others and didn't find them more useful (perhaps the only one I found a bit more useful was "Engineering Thermodynamics" by PK Nag). The common trait of these books when it comes to tapping on the 2nd law is the introduction of the Carno's cycle engine. This is where students are likely about to be confused. The book's scribble in Chapter 7 just adds to the confusion and I found it rather inconsistent with the logical flow of the book up to that point. Then the book continues with Chapter 8 and the concept of "entropy" and leaves it as an abstract quantity that if you want to know (the change in) its value, you can look at the tables at the end of the book!

I had hard time understanding this approach. Why is Carno's cycle even important? The way I was taught the 2nd law by Harry Tiersten years ago, when I had continuum mechanics with him, was through "Caratheodory's axiomatic approach" and that had nothing to do with these imaginary engines what so ever. A nice and beautiful approach which mathematically leads to an expression for the second law, but obviously not a proper way to teach thermo to undergraduate students. It took me a while to realize that the method undertaken by most books on engineering thermodynamics is basically following the historic path through which the thermal sciences have been developed (and to me that’s not necessarily the best method for the sake of teaching). Carno was interested in improving the operation of heat engines, a major challenge at the era of industrialization. What he found using his ideal engine was that the efficiency of reversible heat engines is not due to the consumption of heat energy (what he calls "caloric"), but rather to its transportation from a warm body to a cold body. This is an amazing conclusion, and to me is not trivial at all. This statement was subsequently formulated as the second law of thermodynamics by Lord Kelvin. What Carno postulated (and can be proved easily) was that his ideal reversible engine has the highest possible efficiency; this particular conclusion solved the puzzle for me and provided me a basis to teach the 2nd law. So I raised this question in my class: if the maximum efficiency in a fully reversible engine (no friction, etc) is just controlled by the input and output temperature, then where does the rest of the input energy go to? The answer is, it increases the entropy. At this point I sewed the subject to the molecular picture of gases and tried to relate the entropy to the order in the molecular structure of matters.

Anyhow, while I found teaching thermodynamics a very rewarding experience for myself (and hopefully for my students), I came to the conclusion that the available text books require a major revisit in order to clarify the concept of entropy and improve the explanation of the second law for undergraduate students.



Jayadeep U. B.'s picture

Dear Zhigang,

The major problem with Thermodynamics is the way it is taught (true with Biology also, at least in India!).   As Pradeep told, people appreciate the beauty and "universal applicability" of Thermodynamics only when they study the subject on their own.  I hope I am entering that stage...

The only instance when I wrote a nasty comment in my class notes was when the number of Maxwell relations corssed 50.  I wrote "Congratulations", as if a half-century was scored in "Cricket" (anyway, I am from India!)...

I hope you will post your complete notes in iMechanica.  I am eagerly waiting for it...



Zhigang Suo's picture

Dear Jayadeep:  I know what you meant when you said "people appreciate the beauty and "universal applicability" of Thermodynamics only when they study the subject on their own."  I have been experimenting an approach to teaching thermodynamics, but so far I have had only the opportunity to insert a few lectures in my graduate courses in solid mechanics.  In the Fall 2011 I'll be teaching an undergraduate course on engineering thermodynamics.  I'm excited to have this opportunity to give a subject a try, and am also apprehensive.

An approach I adopted is illustrated in the notes for the first two lectures:

If you happen to have looked at them, I'd like to hear from you.  From your experience of teaching the course, do these notes have a chance for being effective for the first course on engineering thermodynamics?  How can I improve the notes? 

Jayadeep U. B.'s picture

Dear Zhigang,

Sorry that I cannot be of any help in the matter, since I don't have much experience in teaching Thermodynamics, and also not competent enough to make constructive comments in the matter.  I have a Solid Mechanics background, and the interest to "study" Thermodynamics again(!) occurred when I came to know about the concepts behind rubber elasticity.  Of ourse, now I see lot of other reasons (like constitutive relations etc.) for studying Thermodynamics properly...

As mentioned earlier, I am waiting for reading your notes on Thermodynamics...


m_rahman's picture


The books recommended by the previous writers are all good. Sonntag's book is a classic text, which stood the "test of time" by undergoing tens of editions in several languages. Dill and Bloomberg's text is also a good one. I would like to mention few other references of classic nature. The first one is the book called "Theory of Heat" by Maxwell. In my opinion, it should be read by any one wishing to understand the concepts. Next, the book by Keenan is also a good, classic text. Last, the book by Sommerfeld called "Thermodynamics and Statistical Mechanics" is classic masterpiece, written by one of greatest physicists of 20th century. I like his quote on thermodynamics "Thermodynamics is a funny subject. The first time you go through it, you don't understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don't understand it, but by that time you are so used to it, so it doesn't bother you any more".

Mujibur Rahman

Zhigang Suo's picture

Dear Mujibur:  Thank you for all the suggestions.  I'm so delighted that you also like Maxwell's text on Theory of Heat.  I bought the book in 2001 when Dover issued a reprint.  Over the years I have gone back to the book many times for illumination.  I particularly enjoy his descriptions of a large number of experimental observations.  Perhaps one source of difficulty with most modern texts is that they talk about many quantities without telling students how they are measured.  Maxwell's chapters on thermometry and calorimetry are refreshing. 

The book has many more to offer.  The book is also free online.

I borrowed Keenan's book some days ago from the library, but I have not spent much time with it.  I have not heard of Sommerfeld's book, and will check it out.

Have you seen Ingo Muller's History of Thermodynamics?  I saw it in our library today while looking for another book, and am reading it with fun.

m_rahman's picture

Dear Zhigang,

Thanks for the comments. I was unaware of the book by Ingo Muller. I have had a preview of the book from google books, and it looks interesting. I am eager to take a closer look at it.

Another popular book on thermodynamics is a little book called "Understanding Thermodynamics" by Van Ness.

Mujibur Rahman

Libb Thims's picture

I specifically joined iMechanica after reading coming on this thread a few days ago. I haven't read most of the
comments but to put my two cents in, I do happen to have the world's largest
personal collections of thermodynamics books and textbooks, over 300+ at his

The book choice will depend on whether
you are teaching mechanical (Cengel), chemical (Sandler), or bioengineers
(Katchalsky), or physicists (Callen), generally speaking. The most-cited
thermodynamics textbook of all time is Lewis and Randall (1923).

A word of wisdom is to focus on the
underlying core explanation of entropy (transformation content) and entropy
change (equivalence value of all uncompensated transformations) in one heat
cycle as explained by Clausius, in terms of exact differentials, as contrasted
Carnot’s view (Lavoisier-based) of caloric in his model of re-establishment of equilibrium
in the caloric:

Focus on giving a visual picture of
the “working body” (system), as this moved about in the typical Watt steam engine, but more importantly in the original Papin steam engine design. The entire structure of thermodynamics is captured
in the correction Clausius made to the following postulate made by Carnot:

"Whenever work is done by heat (on a body in a cycle) no permanent
change occurs in the condition of the working body
[and that to deny this] would overthrow the whole theory of heat,
of which it is the foundation."

Focus on explaining the “mechanical equivalent of heat” view of heat, as contrasted with
the caloric view of heat, so as to explain how when a body (any body of the
universe) expands and then contracts to its “original condition” that a
permanent change does occur and that this is change is captured mathematically
by the Clausius inequality.

As an end of semester term paper, I would suggest you assign students to write say a
10-page, equation-based, paper on how the universal laws of thermodynamics
apply to human existence. The 400+ thinkers to have attempted such a
formulations over the years are listed here:

and here:|+categorical

I would consider this to be the most
important assignment of one’s college career, in retrospect.

Zhigang Suo's picture

Dear Libb:  Many thanks for the wealth of information and suggestions.  I'll think them over in connection to the class. 

Thank you for pointing out the website Encyclopedia of Human Thermodyanmics.  The page on the plaster model of the surface U(S,V) made by Maxwell is delightful.  I read about the surface in Gibbs's paper about 16 years ago.  I also read about Maxwell's plaster model.  But this is the first time I see a photo of the model.  Wonderful!  I wonder why such a beautiful thing is not shown in any of the major textbooks on Thermodynamics.

The book I prefer for classical thermodynamics is the one by Rogers and Mayhew. It is so well written that I am yet to find a better text than this, not only in thermodynamics but in whole of my engineerin education (I rank book Solid Mechanics by I H Shames second only to this one). But, if this is the first thermodynamics course for your students it may not be appropriate for their self- reading (as it presents  basic laws and applications in different separate parts- this is plausible because author say that thier aim is present a rigrous text to which students may return later in their career for elucidation of fine details). Even then it will definitely help you to decide how to present applications, limitations etc of thermodynamics in most meaningful manner.

Other good bookssuitable for gentle introduction are those by Eastop & McKonkey, Spalding & Coles and the one by Rayner Joel (quite elementary but good on applications).

It is inappropriate to discuss statistical thermodynamics in initial thermo courses (though students may have some ideas of it from physics courses). But, this does not mean that it should not be mentioned at all. Better is to gie them a roadmap of all iour present understanding to make them aware of bigger picture.

Zhigang Suo's picture

Thank you for all the suggestions.  The book by Rogers and Mayhew was also recommended to me by Ravi-Chandar, in November this year, when he and I met in DC.  I bought a copy of the book, and like it.  In particular, I like its descriptions of various cycles.  Many ideas will be useful in teaching the subject.  I plan to spend more time with the book in preparation of the class.

I will also check out other suggestions you made. 

Libb Thims's picture

Glad you liked the surface article. You might also like to get the poster sized
four-step construction of the surface, attached PDF made by Kriz (2008), send
the PDF to Kinkos, and they will print out a nice 38” x 24” giant sized poster
for your classroom. Then you can explain "free energy" to students graphically.

I have one on my wall at home, well worth the printing cost ($45).

Zhigang Suo's picture

Thank you for your comment titled Thermodynamicists nine generations of geneology.  Last night I saw a recent article:

S.I. Sandler and L.V. Woodcock, Historical Observations on Laws of Thermodynamics, Journal of Chemical Engineering Data 55, 4485-4490 (2010).

The articles traces the historical development various laws and principles.  Interestingly, the authors do not restrict themselves to the four laws of thermodynamics, but describe many more key concepts.  Here are a few examples:

  • Hess's law (1840):  Enthalpy is a state function
  • Rankine's law (1855):  Internal energy is a state function
  • Carnot's law (1822):  Entropy is a state function 

This article can be useful in teaching the subject. 

It is always good to have a discussion on the nature of the subject itself before discussing instruction tactics.

Unfortunately, the best descrition of the nature of thermodynamics (to the best o my knowledge) is a pessimistic one. It is due to Sommereld:

"Thermodynamics is a funny subject. The first time you go through it, you
don't understand it at all. The second time you go through it, you
think you understand it, except for one or two small points. The third
time you go through it, you know you don't understand it, but by that
time you are so used to it, so it doesn't bother you any more."

This is so because thermodynamics (in contrast to mechanics) is much less intuitive, much more elegant and requires much more imagination on the part of learner, though it may not be as rigrous or mathematical as mechanics

BEWARE teaching it is not easy (compared with mechanics).

Konstantin Volokh's picture

What a nice description from Sommerfeld!

The hope that thermodynamics will become a clear subject (like mechanics) should not die, especially, in the coming 2011 year.

Happy New Year for iMechanicians!

I have been pondering for quite some time that why we (atleast I) have a feeling of strangeness with thermodynamics? Why is it not that friendly? Mechanics (be it rigid body, solid, fluid, statistical) on the other hand is easily picked once sufficient mathematics is mastered (and sometimes even before that). Same is the case with electromagnetism. Why is thermodynamics so different?

Now the discussion here is so stimulating I will try to add more fuel to it....

Perhaps the answer to my question is that it is almost all right upto the introduction to entropy (almost because coming of enthalpy and to some small extent of internal enery in into the picture also disturbs students). h and s (and later f and g) seem to be the culprits. No amount of meditation on the part of learner seem to relegate the cause. It is not until the statistical sense of these at the molecular level is appreciated that the disturb mind finds peace. I call this phenomenon reversion to mechanics - this time applying it to constituting particles. Randomness is more intuitive than imaginary cycles. Mechanical energy of molecules is more concrete than internal energy of a continuum. So is the difficulty coming from our imagination of non-existent continuum? Surely not! Same assumption is backbone of much more understandable continuum mechanics? Then what is the reason? I still don't know!

Recently, in the introductory lecture of Energy Conversion Systems course, my professor (who is also the father of combustion engineering in my school) asked  the class about the mental picture of entropy. He remained dissatisfied with all our answers from macroscopic to microscopic descriptions. Then he asked us to read about it wherever we find something on it. He told us that he particularly likes the description of entropy given in Saad's book.

I am sure if the order of presentation of microscopic and macroscopic thermodynamics is altered in engineering programs the students will be much happier, provided they can cope up with the elevations in mathematical maturity required. But, it will ruin the beauty of the subject! Is not it surprising that something which never exists and is purely an imaginative feat describes, so precisely and in such a general manner the behaviour of things which really exist!!! This is the beauty of thermodynamics that one can never know that atoms exists and can always have principles which are mostly general.It is independent of actual constitution of matter. This is almost magical!

Zhigang Suo's picture

Many of us who think about Thermodynamics in our spare time (such as during holidays) agonize, at one time or another, about the order in which ideas are presented.  Should we follow more or less historical sequence of discoveries?  Or should we start with microstates and the fundamental postulate?  Should we talk about heat first, or temperature first.  How about both together? 

This agony reminds me of Feynman's Messenger Lectures at Cornell University.  You can read the transcript or watch the video of the lectures.  In particular, I'm thinking of Lecture 2:  The Relation of Mathematics and Physics.

"In Babylonian schools in mathematics the student would learn something by doing a large number of examples until he caught on to the general rule."

"But Euclid discovered that there was a way in which all the theorems of geometry could be ordered from a set of axioms that were particularly simple."

Feynman then went on to explain that "In physics we need the Babylonian method, and not the Euclidian or Greek method."

When we teach a class, however, we have to make a decision where to start.  To save time, we have to present ideas in an orderly sequence.  We become teachers in the Greek tradition.   Perhaps that is why we all feel we have to study thermodynamics many times, and become students in the Babylonian tradition.

After all, few of us can recite the axioms that lead to 13*14 = 182.  But we don't feel mystified.  We have been multiplying numbers all our lives.  Familiarity breads comfort.

Should we talk about heat first, or temperature first.  How about both together?  Maxwell must be a Barbylonian teacher.  In his textbook, Theory of Heat, he first talked about heat and temperature together (Chapter I), and then talked about Thermometry (Chapter II), followed by Calorimetry (Chapter III).  You can buy a copy of this very special book at $13.22, or download a copy for free.

Libb Thims's picture

The Woodcock and Sandler article is a nice read. Woodcock, in fact, sent me a copy back in August. He commented to me that:


“What a great website! I think your [laws of] thermodynamics webpage should have been reference 1 of our paper instead of Peter Atkins [Atkins, Peter. (2007). The Four Laws that Drive the Universe. Oxford University Press]. It’s
a fantastic summary of all the confusion. I am curious to know where
your website is coming from. Who owns and funds it? Who is its intended


What I think Woodcock was getting at is that the laws of thermodynamics, 0-4, were introduced sequentally, in chronological order. Many people get this confused.

Re: mechprog "feeling of strangeness", John Perry and Max Planck mention of entropy as a "Ghostly quantity", seems to have come about because it can only be measured indirectly. Also the great 1902 "what is entropy debate " should appease your mind that the subject was a tenuous one and still is.


   ds = δqrev/T

this is how textbooks usually define entropy. A much more 'lucid' deiniton I found in Anderson,s Modern Compressible flow .


The meaning is same, presentation is much cleaner.

For introducing temperature and heat, I think, best procedure is to do them simultaneously. This approach leaves little room for confusing one with the other.

m_rahman's picture

Interesting point! The question as to which method (Babylonian or Greek) should be followed is connected with philosophical aspects of learning/teaching. Unfortunately (or maybe rather fortunately), there is no single method of teaching, which is the most perfect method. Every good teacher has his/her own good method of teaching. There are however some recommendations out there in the literature. One such recommendation is due to Polya (see his book, Mathematical Discovery, vol. 1, John Wiley, 1962), which is called the “genetic” principle of teaching. The Babylonian method seems to have close semblance to this principle. It is not clear whether Polya himself advanced this idea or some one else, but that’s not important for our discussion. He was certainly responsible for giving currency to this idea, especially in the context of teaching mathematics. The fundamental idea behind this principle is that a good order in which knowledge is acquired by the individual should be the order in which it was acquired by the human race. The principle has been adapted from Ernst Haeckel’s hypothesis: Ontogeny recapitulates Philogeny, which postulates that in developing from embryo to adult, animals go through stages that resemble or represent successive stages in the evolution of their remote ancestors. Put in the context of teaching, it says that the learner would be able to grasp a certain concept lot better if he is exposed to the historical background of that concept. For instance, if the concept is about entropy, it would be good to know who came up with this concept, in what context, how, what would have happened if this concept had not been developed, etc. The learner should be given the opportunity to think about what he would have done in this situation. Even if he is not able to come up with a definitive idea of his own, the very fact that he has delved into it will go a long way in his understanding of the concept. The axiomatic (Greek) approach might be good only after the learner has a good control over the subject. That’s why Maxwell’s book on the theory of heat is so good. It puts the fundamental concepts in a good historical perspective, explains the very concepts so well stripping of the mathematics as much as possible.

It is many times, but not always feasible to teach a subject along the lines of its historical development. There are many instances in which investigators have spent long periods wrestling with the flawed reasoning and recounting each of our ignorance may be time consuming and misleading. For example to discuss all the properties of caloric (the fluidistic picture o heat) before saying that heat is a form of energy in transit may not serve any great purpose (though mentioning it may not do any harm).

Though Prof. Feynman has not acknowledged it, but at times physicists have accepted method of Greek as a characteristic of an elegant physical theory (and yes the whole of mathematics is elegant because o this reason!). There is a great example of this-The Relativity (let us consider the special one), the two elegantly stated axioms are more than enough. We can easily appreciate  books written in Greek style tend to be more compact and indeed 'The  Meaning of Relatiity' is one of the slimmest books! Indeed there are/were physicist (Dirac, Einstein etc) who seek(ed) beauty in equations as if they were mathematician.

I think "Engineering Thermodynamics, Work & Heat Transfer" by Gordon Rogers & Yon Mayhew is best book on Thermodynamics. The approach is very logical and most important fact is in this book 'Principle' was differenciated from 'Application'. It may be highly recommended to study this book in my opinion.

Temesgen Markos's picture

I came across this very beautiful book "Mere Thermodynamics ". In less than 200 small pages it covers a lot of ground. Very clear, physically motivated, and the mathematics is very accessible even for freshmen. I read more than half of it one evening and it was a delight! I got it from the library but I will definitely buy my own copy. 

I would recommend it at least as a suplement. It does not take a lot of time to read it anyway. 

Zhigang Suo's picture

Dear Temesgen:  Following your suggestion, I ordered a copy of the book, which arrived yesterday.  I've gone through it quickly.  It will be an excellent suplement.  Thank you.

The book also reminded me of another very carefully written book: C.J. Adkins, Equilibrium Thermodynamics.  This book can be a good text for a course focussed on classical thermodynamics.  One possible shortcoming of the book is that it uses a large number physical phenomena, which may not be very familiar to engineering students.

Libb Thims's picture

I posted up a quick blog on how to teach thermodynamics, that might be of some assistance.

Libb Thims's picture

Here's an inside look into the minds of two students, which I came across today, who felt they were robbed of classical thermodynamics by a teacher bent on incorporating a statistical mechanics focus in a class whose curriculum was defined as "classical thermodynamics" focus:

I bring this up, because it seems you might be attempting something similar in your class?

Zhigang Suo's picture

Dear Libb:  Thank you for the link.  By now I have looked at several textbooks on engineering thermodynamics:

Each one can be an excellent resource for learning the subject.  I am thinking to select one of them as the main textbook for my course in the Fall 2011, and then augment it with a discussion of the statistical origin of entropy, along the line of my own notes

To accommodate students in bioengineering in the class, I may also need to add a few elements from chemical thermodynamics, such as solutions and electrochemistry.

Mudassir's picture


Respected Teachers I have few questions regarding entropy. 

1) In a reversible adiabatic compression entropy remains the same and in case of irreversible adiabatic compression it increases. Why is it so?

2)Entropy is referred as the disorder of a system. During adiabatic compression gas molecules are compressed and as a result internal energy increases then how can entropy remains constant?

3) How Entropy is a measure of multiplicity of a system and how we relate it with probability?

 I will be very grateful to you all for your help. I am looking forward to hearing from you.



Zhigang Suo's picture

I tried to answer such questions in my notes:

Hope they help.


Zhigang Suo's picture

Thank you all for the input.  I am teaching the course now.  I have decided to use much of the textbook by Borgnakke and Sonntag.  I update an outline after each lecture.

Mudassir's picture

Thanks a lot Sir. Your lectures were extremely informative and helpful. Concept of multiplicity was discussed in detail. I am extremely impressed by your knowledge, insight and grip at the subject, however if you can further elaborate my questions 1 & 2, I shall be very grateful to you.

Zhigang Suo's picture

I'm trying to answer your questions 1 and 2 posted above.

  1. In a reversible adiabatic compression entropy remains the same and in case of irreversible adiabatic compression it increases. Why is it so?
  2. Entropy is referred as the disorder of a system. During adiabatic compression gas molecules are compressed and as a result internal energy increases then how can entropy remains constant?

Here is a superficial answer.  For an adiabatic process of any kind, entopy reamins the same if the process is reversible, and entropy increases if the process is irreversible.  This is just a statement of the second law.  You are probably not looking for an answerof of this kind.  Such an answer never works for me, either, for it does not tell me how things work.

Now a longer answer, basically going back to the basic concepts.  Entropy of a body of gas, by definition, is the logarithm of the number of quantum states.  Entropy is a function of energy and volume, S(U,V).  This function is specific to material, but the trend of the function is readily understood.  When the volume is fixed, the entropy is an increasing function of the energy.  When the energy is fixed, the entropy is an increasing function of the volume.  The two statements can be understood in molecular pictures of the gas

Thus, entropy can remain fixed if a process increases energy but reduces volume.

Now return to your questions.  For an aidiabatic process, no heat is added to the gas.  Thus the energy of the gas increases if work is done to the gas. 

Reversible compression is achieved by a sequence of states of equilibrium, with gradually increasing pressure as the volume of the gas reduces.  During the adiabatic and reversible compression, the energy of the gas increases, but the volume of the gas decreases, such that the entropy remains the same. 

Think of a specific irreversible adabatic compression.  You insulate the gas carfully so that no energy transfers into the gas by heat.  You then place fixed weight on top of the piston.  The wieght remains fixed as the piston moves down, so that weight does more work than in the case of reversible compression.  Thus, the irreversible compression adds more energy to the gas, so that enetroy increases.    

Mudassir's picture

Thanks a lot Sir. I got the answer. By teaching online you are doing a great service to humanity. Keep up the good work.

Respected sir,

I am Ghanshyam. My question is there a thermodynamic property which is nor Intensive nor extensive Property?

Jing_Yang's picture

HI, Prof. Suo:

As we know the thermodynamics are orginally used to describe the equilibrium state of the ideal gas characterized by macroscopic state variables P,V, T, which are uniform at any place inside the gas. But when we consider to apply the framework of thermodynamics to the elastic solids, 

1.Unlike the state variables P, V of gases the state variables stress and strain are not uniform in the elastic solids. In this case, the thermodynamics could still be applied to elastic solids?

2. For elastodynamics of solids, the state variables stress \sigma_{ij} and strain \epsilon_{ij} are function of time t. Does this mean the solids is not in a equlibrium state, and hence the framework of thermodynamics is no longer valid for elastic solids in motion?

Anyway, the thermodynamical analysis of solids in textbooks of continuum mechanics is very common. However, the answers to the above two questions seem to be missed in these books.



I have same question, too.


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