Identifying the Micro behind the Macro

Goggins, Full Capability, and “Atoms First” Thermodynamics

David Goggins, ex-Navy SEAL, now ultra-athlete and motivational speaker, shared in a popular YouTube video (JRE #1212) something that I found incredibly motivating. His biggest fear, and I paraphrase here, is that he arrives at the gates of Heaven and sees God there with a clipboard, holding a list of many great accomplishments. Goggins’ fear is that he looks at this list and says to God, “But that’s not me. I didn’t do those things,” and the all-knowing God replies, “That’s correct. That’s who you could have been. This is a list of all those things you were capable of doing.”

What does Goggins have to do with thermodynamics and, more generally, the subject of education? Nothing and everything. While he has accomplished much in his life, I’m not sure he ever turned his eyes toward thermodynamics. But that’s not the point here. My point is the provocative question that rises from Goggins’ fear. How many students graduate from K-12, college, or grad school without having achieved what they are capable of? How many graduate with a significant gap between who they are and who they could have been? As I recently shared (video here), my short answer for the specific world of university-level thermodynamics is, “too many.” This is unacceptable.

To this end, I believe that each and every university student enrolled in a thermodynamics course is capable of graduating from that course with a solid understanding of thermodynamics. So why isn’t this happening? To me, one of the major reasons lies in the first rung of the multi-step education process: the teacher must understand the material. I don’t believe this is happening for the simple reason that we as educators don’t fully understand thermodynamics.

“The deepest understanding of thermodynamics comes, of course, from understanding the actual machinery underneath.” – Richard Feynman

The understanding I’m referring to is not with the thermodynamic equations and their use to solve problems. The majority of teachers and textbooks already do a very good job teaching this material. What I’m referring to instead is the deep understanding of what the equations physically mean. We simply aren’t there yet as best manifested by the fact that there is no single textbook I’m aware of that presents a physical explanation of thermodynamics based on the motions and interactions of atoms and molecules. Because of this, students learn the equations without understanding what they mean and end up viewing thermodynamics as an indecipherable black box, leaving them intimidated by and so hesitant to use this powerful science. This is their loss as they fall short of who they could be, and this is society’s loss as real-world problems remain unsolved.

The opportunity exists to create a thermodynamics curriculum based on atoms. Employing such an “atoms first” approach will enable students to better learn, better understand, and more confidently employ thermodynamics in a proactive and creative way. The challenge in front of us is to develop this curriculum. Most of the material is already out there in the pages of books and journals and in the minds of many. It needs to be assimilated into one single place. And some of the material remains to be discovered. If students are to reach their full capabilities, we need to gather and create, where needed, this content. This is the task in front of us. Time to start.

Thermodynamic “pain point” results – here are your responses

I believe that a better understanding of thermodynamics is available by explaining the connections between the micro-world of moving and colliding atoms that attract and repel each other and the macro-world of classical thermodynamics. My goal is to identify and clarify such micro-to-macro connections. To ensure that I’m addressing true needs of the science community, I reached out to you all at the beginning of this year (here) to seek your personal “pain points” with thermodynamics. I asked, what are the stumbling blocks you encounter when trying to teach or learn the physical meanings behind thermodynamic equations and phenomena? Presented below are your responses. My thanks to those who engaged in this exercise.

If you feel you can address any items on the list with supportive references, could you please let me know? rthanlon@mit.edu

Based on a review of these responses, and subsequent discussions with some of you, I have decided to begin this journey by focusing on a single, specific phenomenon, the Joule-Thomson effect, number 13 in the list below. I hope to have some results to share with you in my next post.

A final note. One responder asked me, how can you animate thermodynamic concepts so that students can understand them? How can you translate physical chemistry and thermodynamics into practical real-world audiovisual content? If any of you has ideas on this, please let me know.

_ _ _ _ _

Explain the physical meaning of not only temperature, but also energy, entropy, enthalpy, exergy, Gibbs energy, and the dreaded fugacity.
Speaking of which, what exactly is fugacity and how does it relate to the material world?
What is the physical mechanism behind the existence of the critical point?
What does the concept of energy minimization physically mean, and how is this applied in the form of Gibbs free energy minimization of protein folding?
Reversibility: What is it (really) and why is it important?
What is the fundamental physical cause of the temperature effects that result when you depressurize a gas cylinder?
Explain the presence of heterogeneous azeotropes.
How deep a vacuum on steam turbines is worthwhile to pursue? How can this be more quickly understood and appreciated?
Van der Waals equation. Why does long range attraction and short range repulsion give a liquid (ie phase transition), beyond just saying, “It’s in the math”? Does this same phenomenon hold with colloids and polymers in solution, that they undergo a “vapor-liquid type phase transition”?
Column of gas in a gravitational field. Is it isothermal or is there a temperature gradient, and why? James Clerk Maxwell and Ludwig Boltzmann assumed the former, Josef Loschmidt the latter. Who was right?
Where does thermodynamics begin? Is a perfect vacuum really a thermodynamic system? Without molecules, do we have pressure, temperature, Q, W, S & H?
Gas Phase Behavior – ideal and non-ideal. Given that all atoms/molecules attract all atoms/molecules via London dispersion forces, what is it that makes a gas behave ideal in which such attraction has negligible influence? What is the dividing line between “ideal gas” and “non-ideal gas”? Some have suggested that it is the formation of dimers the causes of deviation from ideal gas law, but I have yet to find conclusive evidence of this in the literature.
Joule-Thomson Effect – explain this. This effect is naturally related to the combined effects of intermolecular attraction and repulsion. But how exactly does this work at the molecular level? How does this explain, for example, no effect for ideal gas, heating effect for hydrogen, and the presence of an inversion temperature?
Gas – flow. Explain in plain English Bernoulli’s equation, especially the trade-off between pressure and flow velocity.
Photons. When are photons released? Solely with the acceleration of charges? Does this always release photons? As an unbound electron accelerates towards a single proton, are photons released? How about during chemical reactions? Because chemical reactions involve a change in energy level of electrons, are photons always released? If so, should photons be included in reaction equations? When photons are absorbed, heat is generated in the form of an increase in temperature. What is the energy balance around photon absorption (and emission)? What is the physical event that leads to an increase in kinetic energy of the atoms that absorb the photon? When does the presence of photons influence reaction equilibrium?
Explain the micro-physics behind the Stefan-Boltzmann T⁴ law of radiation.
Explain the micro-physics behind the existence of a supercritical fluid.
Explain the Clausius-Clapeyron Equation in plain English. Why is it what it is?
Gas Phase Reactions – Walk through exactly what happens at the atomic scale during reaction. For example, picture two hydrogen atoms. Long-range attraction draws each towards the other. But up close, the strong electron repulsion pushes them apart. How is this repulsive force overcome so that reaction occurs? Also, “heat” is generated when two hydrogen atoms combine to form molecular hydrogen. What exactly does this mean? What specific physical events lead to an increase in the kinetic energy of the atoms comprising the H-atom gas system when they react? Also, are photons emitted as a result of this reaction?
What exactly does the change in Gibbs energy of a chemical reaction quantify? Is it simply the total change in energy of the orbital electrons?
Why isn’t the distribution of orbital electrons included in the Boltzmann definition of entropy? If a chemical reaction is really the distribution of orbital electrons into their most probable distribution, shouldn’t the change in entropy account for this?
Phase Change – Vapor/Liquid (similar discussion for liquid/solid). How does phase change occur? Walk through each step involved in energy balance. Also, walk through condensation. How does an atom/molecule slow down enough to be ‘captured’ by another atom/molecule? Do the slow atoms/molecules at the left end (slower speed) of the statistical distribution condense first? (Same could be asked of chemical reactions. Do the fast atoms/molecules at the right end of the statistical distribution react first?) When an atom escapes from liquid to vapor, what velocity does it end with? Is the resulting vapor initially at a very low temperature due to escape and then is this why some thermal energy is needed to bring the escaped gas up to temperature of the liquid? Also, does the average velocity of particles in vapor fall short of their average velocity in liquid, especially in case the liquid is a solution and the vapor pressure at a given temperature of the liquid is hence reduced?
Absolute zero. Yes, the entropy of a pure crystal is zero at absolute zero. But aren’t the electrons still in motion? And wouldn’t this mean that the polarity of the atoms is not constant at absolute zero, and instead varies, and wouldn’t this result in a variation of attraction and hence result in motion, which is inconsistent with the concept of absolute zero? So what does matter physically look like at absolute zero?

END

What are your personal “pain points” with thermodynamics?

What are your personal “pain points” with thermodynamics? What are the stumbling blocks you encounter when trying to understand the physical meaning behind such thermodynamic equations and phenomena as Gibbs Free Energy, Joule-Thomson expansion, phase change, and even the physical properties of matter, including heat capacity and absolute temperature? Could you please share these with me in the comments section below or via direct email (rthanlon@mit.edu), and I’ll add them to my own list of stumbling blocks and unanswered questions. My objective in doing this is as follows.

I believe that a better understanding of thermodynamics is available by explaining the connections between the micro-world of moving and colliding atoms and the macro-world of classical thermodynamics. My goal is to identify and clarify the micro-to-macro connections for the final list of “paint points” generated here, this list serving to ensure I’m addressing true needs of the science community. I remain undecided on how best to share these results back to you all. It may be a 2nd book, creation of a special YouTube channel, or some other form. Again, not sure. Regardless, a long journey awaits, and I’m looking forward to it.

If you have ideas on where best to locate well documented micro-to-macro connections, please let me know. My starting point is Richard Feynman’s excellent “Lectures on Physics” but even there, while some of my own pain points are indeed addressed, many aren’t.

Professors & teachers – please consider sharing this with your colleagues and also with your current or past students. I’d be very interested to hear their take on things.

Wishing each of you well for 2022.

Thank you,
Bob

The Road to Entropy – Boltzmann and his probabilistic entropy

Ludwig Boltzmann (1844-1906) brought his mastery of mathematics to the kinetic theory of gases and provided us with our first mechanical understanding of entropy. To Boltzmann, his work proved that entropy ALWAYS increases or remains constant. But to others, most notably Josef Loschmidt (1821-1895), his work contained a paradox that needed to be addressed. Loschmidt asked a provocative question about this paradox that motivated Boltzmann to transform his mathematics from mechanics to probability. The end result was a probabilistic entropy: entropy ALMOST ALWAYS increases. What was the question? Watch to find out.

For an excellent in-depth analysis of the development of the kinetic theory of gases and Boltzmann’s connection of entropy to the movement of the hypothesized atoms and molecules, I highly recommend Stephen Brush’s Kinetic Theory of Gases, The: An Anthology of Classic Papers with Historical Commentary.

I delve into the mathematical details of Boltzmann’s work, and also the personal details of his battle to defend his work, in my book.

The Road to Entropy – The kinetic theory of gases & heat capacity

I believe that an improved approach to teaching thermodynamics can be created by starting with the atomic theory of matter and then explaining the connections between this theory and macroscopic thermodynamic phenomena. This micro-to-macro approach arguably began in the late 19th century when a small group of scientists, namely Rudolf Clausius, James Clerk Maxwell, and Ludwig Boltzmann, successfully developed the kinetic theory of gases, which eventually became the key bridge from classical thermodynamics to statistical mechanics. The prediction of heat capacity played a crucial role in this effort, and an interesting related story was the absence of heat capacity predictions for monatomic elements. Why was this? To me, the reason had to do with the structural difference between a sphere and an atom. Check out the below video in which I lay out my argument.

Addendum: It’s a real challenge trying to understand what the early theorists were truly thinking as they developed thermodynamics. I wish each had written an autobiography to share their thoughts, thoughts that were not suitable for publication but still, their own thoughts on what nature looked like. Especially Gibbs!

Regarding the heat capacity of gas atoms, it’s not that they attempted and made a mistake, it’s that they never attempted to begin with, and this is what struck me when I read their papers. I believe that the main reason for this is that they couldn’t conceive of an atom that didn’t spin, or have energy associated with spin. They couldn’t conceive of an atom comprised of mostly empty space, with all the mass concentrated in the center nucleus.

For an excellent in-depth analysis of the development of the kinetic theory of gases, I highly recommend Stephen Brush’s Kinetic Theory of Gases, The: An Anthology of Classic Papers with Historical Commentary.

I delve into the successful development of the kinetic theory of gases, which successive chapters on Clausius, then Maxwell, and finally Boltzmann, in my book.

The Road to Entropy – Clausius, Gibbs, and increasing entropy

At the conclusion of his famed 1865 paper announcing the discovery of a new property of matter that he named entropy, Rudolf Clausius stated: the entropy of the universe tends to a maximum. This statement came as a total surprise to me as there was no prior supportive discussion behind it, and it had me wondering whether or not Clausius truly understood its meaning. Fortunately for us, someone else did understand its meaning as manifested by the fact that this person evolved this statement into one more critically relevant to thermodynamics: the entropy of an isolated system increases to a maximum. The person? J. Willard Gibbs. To understand how this came about, check out this video.

I go into much more depth on the combined work of Clausius and Gibbs in my book Block by Block – The Historical and Theoretical Foundations of Thermodynamics.

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The Road to Entropy – Clausius undaunted

Have you ever experienced that wondrous “Eureka!” moment of insight when you’ve discovered some hidden secret of nature? Archimedes did when he realized that the volume of water displaced is equal to the volume of the body submerged. Kekulé did when discovered benzene’s structure. Hubble did when he discovered that the stars are all moving away from us at speeds that increase with distance. And Rudolf Clausius arguably did when he realized that he could correct Sadi Carnot’s “flawed” masterpiece (here) by replacing the caloric theory of heat with James Joule’s theory of work-heat equivalence (here). Clausius’s 1850 publication on this topic gave us the 1st Law of Thermodynamics. I capture the essence of Clausius’s realization in this video.

Carnot’s original work together with Clausius’s 1850 publication are captured well in this book:

Carnot, Sadi, E Clapeyron, and R Clausius. 1988. *Reflections on the Motive Power of Fire by Sadi Carnot and Other Papers on the Second Law of Thermodynamics by E. Clapeyron and R. Clausius. Edited with an Introduction by E. Mendoza.* Edited by E Mendoza. Mineola (N.Y.): Dover.

I go into much more depth on Clausius’s 1850 publication in my book Block by Block – The Historical and Theoretical Foundations of Thermodynamics.

The Road to Entropy – James Joule and the power of his curiosity (video)

James Joule could have observed what he did and then done nothing with it. Instead, he became driven to understand and explain it and so discovered the mechanical equivalent of heat, a forerunner of the concept of energy and the 1st law of Thermodynamics. His story is a good one, an inspiring one, an example of how good science is conducted and how a good scientist behaves. I share a piece of his story here in this video.

I go into much more detail about the life of James Joule, including his wonderful collaboration with William Thomson, later Lord Kelvin, in my book Block by Block – The Historical and Theoretical Foundations of Thermodynamics.

The Road to Entropy – Sadi Carnot’s use of analogy to create his “flawed” masterpiece (video)

The commercialization of the high-pressure steam engines by the Cornish Engineers of Britain inspired Sadi Carnot, a French military engineer, to analyze these engines and seek the theories to guide their improvement.

If you’re interested in doing a deep dive into Sadi Carnot’s work, here are two excellent references.

Carnot, Sadi. 1986. Reflexions on the Motive Power of Fire. Edited and translated by Robert Fox. University Press.

I go into much more depth on Sadi Carnot’s work, including a detailed analysis of his eponymous heat cycle, in my book Block by Block – The Historical and Theoretical Foundations of Thermodynamics.

The oldest surviving steam engine is on display at the Henry Ford Museum of Innovation in Michigan

I was traveling in Michigan this past week and took a day to visit the Henry Ford Museum of Innovation. All I can say is, WOW! Together with the adjacent Greenfield Village, well worth the visit.

The Innovation Museum offers great displays of engine technologies, including the oldest surviving steam engine in the world, a 1760-ish Newcomen engine, which was given to Henry Ford from the Earl of Stamford in 1929. The photograph is of me standing next to this large machine. The fact that these displays were just one part of the larger museum is remarkable. Again, well worth the visit.